updated Knowledge/DiffApp.thy isac-update-Isa09-2
authorWalther Neuper <neuper@ist.tugraz.at>
Wed, 08 Sep 2010 17:49:36 +0200
branchisac-update-Isa09-2
changeset 37995fac82f29f143
parent 37994 eb4c556a525b
child 37996 eb7d9cbaa3ef
updated Knowledge/DiffApp.thy
src/Tools/isac/Build_Isac.thy
src/Tools/isac/Knowledge/DiffApp-oldscr.sml
src/Tools/isac/Knowledge/DiffApp.sml
src/Tools/isac/Knowledge/DiffApp.thy
src/Tools/isac/Knowledge/EqSystem.thy
test/Tools/isac/Knowledge/diffapp.sml
test/Tools/isac/Knowledge/eqsystem.sml
     1.1 --- a/src/Tools/isac/Build_Isac.thy	Wed Sep 08 17:20:03 2010 +0200
     1.2 +++ b/src/Tools/isac/Build_Isac.thy	Wed Sep 08 17:49:36 2010 +0200
     1.3 @@ -78,16 +78,16 @@
     1.4  use_thy "Knowledge/Calculus"
     1.5  use_thy "Knowledge/Trig"
     1.6  use_thy "Knowledge/LogExp"
     1.7 -
     1.8  use_thy "Knowledge/Diff"
     1.9  
    1.10 -ML {* 
    1.11 +use_thy "Knowledge/DiffApp"
    1.12 +
    1.13 +ML {* 111;
    1.14  *}
    1.15  
    1.16  
    1.17  text {*------------------------------------------*}
    1.18  (*
    1.19 -use_thy "Knowledge/DiffApp"
    1.20  use_thy "Knowledge/Integrate"
    1.21  use_thy "Knowledge/EqSystem"
    1.22  use_thy "Knowledge/Biegelinie"
     2.1 --- a/src/Tools/isac/Knowledge/DiffApp-oldscr.sml	Wed Sep 08 17:20:03 2010 +0200
     2.2 +++ b/src/Tools/isac/Knowledge/DiffApp-oldscr.sml	Wed Sep 08 17:49:36 2010 +0200
     2.3 @@ -7,32 +7,32 @@
     2.4  ML> ...
     2.5  ML> val c = (the o (parse thy)) s; 
     2.6  val c =
     2.7 -  "Script1 Maximum_value fix_ m_ rs_ v_v itv_ err_ =
     2.8 -    let e_e = (hd o filter (Testvar m_)) rs_;
     2.9 +  "Script1 Maximum_value f_ix m_ r_s v_v itv_ err_ =
    2.10 +    let e_e = (hd o filter (Testvar m_)) r_s;
    2.11          t_ =
    2.12 -          if #1 < Length rs_
    2.13 -          then make_fun (R, [make, function], no_met) m_ v_v rs_
    2.14 -          else (Lhs o hd) rs_;
    2.15 +          if #1 < Length r_s
    2.16 +          then make_fun (R, [make, function], no_met) m_ v_v r_s
    2.17 +          else (Lhs o hd) r_s;
    2.18          mx_ =
    2.19            max_on_interval (R, [on_interval, max_of, function],
    2.20                             maximum_on_interval) t_ v_v itv_
    2.21      in find_vals (R, [find_values, tool], find_values)
    2.22 -       mx_ t_ v_v m_ dropWhile (op = e_e) rs_" : cterm
    2.23 +       mx_ t_ v_v m_ dropWhile (op = e_e) r_s" : cterm
    2.24  
    2.25  ML> set show_types;
    2.26  ML> c;
    2.27  val c =
    2.28 -  "Script1 Maximum_value fix_::bool list m_::real rs_::bool list v_v::real itv_v::real set err_::bool =
    2.29 -    let e_e::bool = (hd o filter (Testvar m_)) rs_;
    2.30 +  "Script1 Maximum_value f_ix::bool list m_::real r_s::bool list v_v::real itv_v::real set err_::bool =
    2.31 +    let e_e::bool = (hd o filter (Testvar m_)) r_s;
    2.32          t_::real =
    2.33 -          if (#1::real) < Length rs_
    2.34 -          then make_fun (R::ID, [make::ID, function::ID], no_met::ID) m_ v_v rs_
    2.35 -          else (Lhs o hd) rs_;
    2.36 +          if (#1::real) < Length r_s
    2.37 +          then make_fun (R::ID, [make::ID, function::ID], no_met::ID) m_ v_v r_s
    2.38 +          else (Lhs o hd) r_s;
    2.39          mx_::real =
    2.40            max_on_interval (R, [on_interval::ID, max_of::ID, function],
    2.41                             maximum_on_interval::ID) t_ v_v itv_
    2.42      in find_vals (R, [find_values::ID, tool::ID], find_values)
    2.43 -       mx_ t_ v_v m_ dropWhile (op = e_e) rs_" : cterm
    2.44 +       mx_ t_ v_v m_ dropWhile (op = e_e) r_s" : cterm
    2.45  
    2.46  
    2.47  
    2.48 @@ -44,20 +44,20 @@
    2.49  ML> val c = (the o (parse thy)) s; 
    2.50  val c =
    2.51    "Script maximum =
    2.52 -    Input [Bool fix_, Real m_, BoolList rs_, Real v_v, RealSet itv_, Bool err_]
    2.53 -    Local [Bool e_e, Real t_, Real mx_, RealList vs_]
    2.54 +    Input [Bool f_ix, Real m_, BoolList r_s, Real v_v, RealSet itv_, Bool err_]
    2.55 +    Local [Bool e_e, Real t_, Real mx_, RealList v_s]
    2.56      Tacs [SEQU
    2.57 -           [let e_e = (hd o filter (Testvar m_)) rs_
    2.58 -            in if #1 < Length rs_
    2.59 +           [let e_e = (hd o filter (Testvar m_)) r_s
    2.60 +            in if #1 < Length r_s
    2.61                 then Subproblem Spec (R, [make, function], no_met)
    2.62 -                     InOut [In m_, In v_v, In rs_, Out t_]
    2.63 -               else t_ := (Lhs o hd) rs_ ;
    2.64 +                     InOut [In m_, In v_v, In r_s, Out t_]
    2.65 +               else t_ := (Lhs o hd) r_s ;
    2.66              Subproblem Spec (R, [on_interval, max_of, function],
    2.67                               maximum_on_interval)
    2.68               InOut [In t_, In v_v, In itv_, In err_, Out mx_] ;
    2.69              Subproblem Spec (R, [find_values, tool], find_values)
    2.70 -             InOut [In mx_, In t_, In v_v, In m_, In (dropWhile (op = e_e) rs_),
    2.71 -                    Out vs_]]]
    2.72 +             InOut [In mx_, In t_, In v_v, In m_, In (dropWhile (op = e_e) r_s),
    2.73 +                    Out v_s]]]
    2.74      Return []" : cterm
    2.75  
    2.76  ML> ...
    2.77 @@ -65,11 +65,11 @@
    2.78  val c =
    2.79    "Script make_fun_by_new_variable =
    2.80      Input [Real f_f, Real v_v, BoolList eqs]
    2.81 -    Local [Bool h_, BoolList es_, RealList vs_, Real v1_, Real v2_, Bool e1,
    2.82 +    Local [Bool h_, BoolList es_, RealList v_s, Real v1_, Real v2_, Bool e1,
    2.83             Bool e2_, BoolList s_1, BoolList s_2]
    2.84      Tacs [SEQU
    2.85             [let h_ = (hd o filter (Testvar m_)) eqs; es_ = eqs -- [h_];
    2.86 -                vs_ = Var h_ -- [f_]; v1_ = Nth #1 vs_; v2_ = Nth #2 vs_;
    2.87 +                v_s = Var h_ -- [f_]; v1_ = Nth #1 v_s; v2_ = Nth #2 v_s;
    2.88                  e1_ = (hd o filter (Testvar v1_)) es_;
    2.89                  e2_ = (hd o filter (Testvar v2_)) es_
    2.90              in Subproblem Spec (R, [univar, equation], no_met)
    2.91 @@ -85,10 +85,10 @@
    2.92  val c =
    2.93    "Script make_fun_explicit =
    2.94      Input [Real f_f, Real v_v, BoolList eqs]
    2.95 -    Local [Bool h_, Bool eq_, RealList vs_, Real v1_, BoolList ss_]
    2.96 +    Local [Bool h_, Bool eq_, RealList v_s, Real v1_, BoolList ss_]
    2.97      Tacs [SEQU
    2.98             [let h_ = (hd o filter (Testvar m_)) eqs; eq_ = hd (eqs -- [h_]);
    2.99 -                vs_ = Var h_ -- [f_]; v1_ = hd (vs_ -- [v_])
   2.100 +                v_s = Var h_ -- [f_]; v1_ = hd (v_s -- [v_])
   2.101              in Subproblem Spec (R, [univar, equation], no_met)
   2.102                  InOut [In eq_, In v1_, Out ss_]],
   2.103            Take (Bool h_) ; Substitute [(v1_, (Rhs o hd) ss_)]]
     3.1 --- a/src/Tools/isac/Knowledge/DiffApp.sml	Wed Sep 08 17:20:03 2010 +0200
     3.2 +++ b/src/Tools/isac/Knowledge/DiffApp.sml	Wed Sep 08 17:49:36 2010 +0200
     3.3 @@ -14,13 +14,13 @@
     3.4  [
     3.5   prep_pbt DiffAppl.thy
     3.6   (["DiffAppl","maximum_of","function"],
     3.7 -  [("#Given" ,"fixedValues fix_"),
     3.8 +  [("#Given" ,"fixedValues f_ix"),
     3.9     ("#Find"  ,"maximum m_"),
    3.10 -   ("#Find"  ,"valuesFor vs_"),
    3.11 -   ("#Relate","relations rs_")  (*,
    3.12 -   ("#where" ,"foldl (op&) True (map (Not o ((op<=) #0) o Rhs) fix_)"),
    3.13 -   ("#with"  ,"Ex_frees ((foldl (op &) True rs_) &  \
    3.14 -    \ (ALL m'. (subst (m_,m') (foldl (op &) True rs_) \
    3.15 +   ("#Find"  ,"valuesFor v_s"),
    3.16 +   ("#Relate","relations r_s")  (*,
    3.17 +   ("#where" ,"foldl (op&) True (map (Not o ((op<=) #0) o Rhs) f_ix)"),
    3.18 +   ("#with"  ,"Ex_frees ((foldl (op &) True r_s) &  \
    3.19 +    \ (ALL m'. (subst (m_,m') (foldl (op &) True r_s) \
    3.20      \            --> m' <= m_)))")    *)
    3.21    ]),
    3.22  
    3.23 @@ -37,7 +37,7 @@
    3.24    [("#Given" ,"functionTerm t_"),
    3.25     ("#Given" ,"boundVariable v_v"),
    3.26     ("#Given" ,"interval itv_"),
    3.27 -   ("#Find"  ,"maxArgument v_0_")
    3.28 +   ("#Find"  ,"maxArgument v_0")
    3.29    ]),
    3.30  
    3.31   prep_pbt DiffAppl.thy
    3.32 @@ -46,7 +46,7 @@
    3.33     ("#Given" ,"functionTerm f_f"),
    3.34     ("#Given" ,"boundVariable v_v"),
    3.35     ("#Find"  ,"valuesFor vls_"),
    3.36 -   ("#Relate","additionalRels rs_")
    3.37 +   ("#Relate","additionalRels r_s")
    3.38    ])
    3.39  ]);
    3.40  
    3.41 @@ -55,13 +55,13 @@
    3.42  [
    3.43   (("DiffAppl","max_by_calculus"):metID,
    3.44    {ppc = prep_met DiffAppl.thy
    3.45 -   [("#Given" ,"fixedValues fix_"),
    3.46 +   [("#Given" ,"fixedValues f_ix"),
    3.47      ("#Given" ,"boundVariable v_v"),
    3.48      ("#Given" ,"interval itv_"),
    3.49      ("#Given" ,"errorBound err_"),
    3.50      ("#Find"  ,"maximum m_"),
    3.51 -    ("#Find"  ,"valuesFor vs_"),
    3.52 -    ("#Relate","relations rs_")
    3.53 +    ("#Find"  ,"valuesFor v_s"),
    3.54 +    ("#Relate","relations r_s")
    3.55      ],
    3.56     rew_ord'="tless_true",rls'="eval_rls",asm_rls=[],asm_thm=[],
    3.57     scr=EmptyScr} : met),
    3.58 @@ -92,7 +92,7 @@
    3.59      ("#Given" ,"boundVariable v_v"),
    3.60      ("#Given" ,"interval itv_"),
    3.61      ("#Given" ,"errorBound err_"),
    3.62 -    ("#Find"  ,"maxArgument v_0_")
    3.63 +    ("#Find"  ,"maxArgument v_0")
    3.64      ],
    3.65     rew_ord'="tless_true",rls'="eval_rls",asm_rls=[],asm_thm=[],
    3.66     scr=EmptyScr} : met),
     4.1 --- a/src/Tools/isac/Knowledge/DiffApp.thy	Wed Sep 08 17:20:03 2010 +0200
     4.2 +++ b/src/Tools/isac/Knowledge/DiffApp.thy	Wed Sep 08 17:49:36 2010 +0200
     4.3 @@ -29,8 +29,8 @@
     4.4    filterVar :: "[real, 'a list] => 'a list"
     4.5  
     4.6  (*primrec*)axioms
     4.7 -  filterVar_Nil		"filterVar v []     = []"
     4.8 -  filterVar_Const	"filterVar v (x#xs) =                       
     4.9 +  filterVar_Nil:		"filterVar v []     = []"
    4.10 +  filterVar_Const:	"filterVar v (x#xs) =                       
    4.11  			 (if (v mem (Vars x)) then x#(filterVar v xs)  
    4.12  			                    else filterVar v xs)   "
    4.13  text {*WN.6.5.03: old decisions in this file partially are being changed
    4.14 @@ -80,16 +80,17 @@
    4.15  		(!ruleset',
    4.16  		 [("eval_rls",Atools_erls)(*FIXXXME:del with rls.rls'*)
    4.17  		  ]);
    4.18 -
    4.19 +*}
    4.20 +ML{*
    4.21  
    4.22  (** problem types **)
    4.23  
    4.24  store_pbt
    4.25   (prep_pbt thy "pbl_fun_max" [] e_pblID
    4.26   (["maximum_of","function"],
    4.27 -  [("#Given" ,["fixedValues fix_"]),
    4.28 -   ("#Find"  ,["maximum m_","valuesFor vs_"]),
    4.29 -   ("#Relate",["relations rs_"])
    4.30 +  [("#Given" ,["fixedValues f_ix"]),
    4.31 +   ("#Find"  ,["maximum m_m","valuesFor v_s"]),
    4.32 +   ("#Relate",["relations r_s"])
    4.33    ],
    4.34    e_rls, NONE, []));
    4.35  
    4.36 @@ -97,14 +98,14 @@
    4.37   (prep_pbt thy "pbl_fun_make" [] e_pblID
    4.38   (["make","function"]:pblID,
    4.39    [("#Given" ,["functionOf f_f","boundVariable v_v","equalities eqs"]),
    4.40 -   ("#Find"  ,["functionEq f_1_"])
    4.41 +   ("#Find"  ,["functionEq f_1"])
    4.42    ],
    4.43    e_rls, NONE, []));
    4.44  store_pbt
    4.45   (prep_pbt thy "pbl_fun_max_expl" [] e_pblID
    4.46   (["by_explicit","make","function"]:pblID,
    4.47    [("#Given" ,["functionOf f_f","boundVariable v_v","equalities eqs"]),
    4.48 -   ("#Find"  ,["functionEq f_1_"])
    4.49 +   ("#Find"  ,["functionEq f_1"])
    4.50    ],
    4.51    e_rls, NONE, [["DiffApp","make_fun_by_explicit"]]));
    4.52  store_pbt
    4.53 @@ -112,16 +113,16 @@
    4.54   (["by_new_variable","make","function"]:pblID,
    4.55    [("#Given" ,["functionOf f_f","boundVariable v_v","equalities eqs"]),
    4.56     (*WN.12.5.03: precond for distinction still missing*)
    4.57 -   ("#Find"  ,["functionEq f_1_"])
    4.58 +   ("#Find"  ,["functionEq f_1"])
    4.59    ],
    4.60    e_rls, NONE, [["DiffApp","make_fun_by_new_variable"]]));
    4.61  
    4.62  store_pbt
    4.63   (prep_pbt thy "pbl_fun_max_interv" [] e_pblID
    4.64   (["on_interval","maximum_of","function"]:pblID,
    4.65 -  [("#Given" ,["functionEq t_","boundVariable v_v","interval itv_"]),
    4.66 +  [("#Given" ,["functionEq t_t","boundVariable v_v","interval i_tv"]),
    4.67     (*WN.12.5.03: precond for distinction still missing*)
    4.68 -   ("#Find"  ,["maxArgument v_0_"])
    4.69 +   ("#Find"  ,["maxArgument v_0"])
    4.70    ],
    4.71    e_rls, NONE, []));
    4.72  
    4.73 @@ -134,12 +135,14 @@
    4.74  store_pbt
    4.75   (prep_pbt thy "pbl_tool_findvals" [] e_pblID
    4.76   (["find_values","tool"]:pblID,
    4.77 -  [("#Given" ,["maxArgument ma_","functionEq f_f","boundVariable v_v"]),
    4.78 -   ("#Find"  ,["valuesFor vls_"]),
    4.79 -   ("#Relate",["additionalRels rs_"])
    4.80 +  [("#Given" ,["maxArgument m_ax","functionEq f_f","boundVariable v_v"]),
    4.81 +   ("#Find"  ,["valuesFor v_ls"]),
    4.82 +   ("#Relate",["additionalRels r_s"])
    4.83    ],
    4.84    e_rls, NONE, []));
    4.85  
    4.86 +*}
    4.87 +ML{*
    4.88  
    4.89  (** methods, scripts not yet implemented **)
    4.90  
    4.91 @@ -150,89 +153,99 @@
    4.92     {rew_ord'="tless_true",rls'=Atools_erls,calc = [], srls = e_rls, prls=e_rls,
    4.93      crls = Atools_erls, nrls=norm_Rational
    4.94      (*, asm_rls=[],asm_thm=[]*)}, "empty_script"));
    4.95 +*}
    4.96 +ML{*
    4.97  store_met
    4.98   (prep_met thy "met_diffapp_max" [] e_metID
    4.99   (["DiffApp","max_by_calculus"]:metID,
   4.100 -  [("#Given" ,["fixedValues fix_","maximum m_","relations rs_",
   4.101 -	       "boundVariable v_v","interval itv_","errorBound err_"]),
   4.102 -    ("#Find"  ,["valuesFor vs_"]),
   4.103 +  [("#Given" ,["fixedValues f_ix","maximum m_m","relations r_s",
   4.104 +	       "boundVariable v_v","interval i_tv","errorBound e_rr"]),
   4.105 +    ("#Find"  ,["valuesFor v_s"]),
   4.106      ("#Relate",[])
   4.107      ],
   4.108    {rew_ord'="tless_true",rls'=eval_rls,calc=[],srls=list_rls,prls=e_rls,
   4.109      crls = eval_rls, nrls=norm_Rational
   4.110     (*,  asm_rls=[],asm_thm=[]*)},
   4.111 -  "Script Maximum_value(fix_::bool list)(m_::real) (rs_::bool list)       " ^
   4.112 -  "      (v_v::real) (itv_v::real set) (err_::bool) =                       " ^ 
   4.113 -  " (let e_e = (hd o (filterVar m_)) rs_;                                  " ^
   4.114 -  "      t_ = (if 1 < length_ rs_                                         " ^
   4.115 -  "           then (SubProblem (DiffApp_,[make,function],[no_met])        " ^
   4.116 -  "                     [REAL m_, REAL v_v, BOOL_LIST rs_])             " ^
   4.117 -  "           else (hd rs_));                                             " ^
   4.118 -  "      (mx_::real) =                                                    " ^ 
   4.119 -  "SubProblem(DiffApp_,[on_interval,maximum_of,function],                 " ^
   4.120 +  "Script Maximum_value(f_ix::bool list)(m_m::real) (r_s::bool list)       " ^
   4.121 +  "      (v_v::real) (itv_v::real set) (e_rr::bool) =                       " ^ 
   4.122 +  " (let e_e = (hd o (filterVar m_m)) r_s;                                  " ^
   4.123 +  "      t_t = (if 1 < LENGTH r_s                                         " ^
   4.124 +  "           then (SubProblem (DiffApp',[make,function],[no_met])        " ^
   4.125 +  "                     [REAL m_m, REAL v_v, BOOL_LIST r_s])             " ^
   4.126 +  "           else (hd r_s));                                             " ^
   4.127 +  "      (m_x::real) =                                                    " ^ 
   4.128 +  "SubProblem(DiffApp',[on_interval,maximum_of,function],                 " ^
   4.129    "                                [DiffApp,max_on_interval_by_calculus]) " ^
   4.130 -  "                               [BOOL t_, REAL v_v, REAL_SET itv_]    " ^
   4.131 -  " in ((SubProblem (DiffApp_,[find_values,tool],[Isac,find_values])      " ^
   4.132 -  "      [REAL mx_, REAL (Rhs t_), REAL v_v, REAL m_,                  " ^
   4.133 -  "       BOOL_LIST (dropWhile (ident e_e) rs_)])::bool list))            "
   4.134 +  "                               [BOOL t_t, REAL v_v, REAL_SET i_tv]    " ^
   4.135 +  " in ((SubProblem (DiffApp',[find_values,tool],[Isac,find_values])      " ^
   4.136 +  "      [REAL m_x, REAL (Rhs t_t), REAL v_v, REAL m_m,                  " ^
   4.137 +  "       BOOL_LIST (dropWhile (ident e_e) r_s)])::bool list))            "
   4.138   ));
   4.139 +*}
   4.140 +ML{*
   4.141  store_met
   4.142   (prep_met thy "met_diffapp_funnew" [] e_metID
   4.143   (["DiffApp","make_fun_by_new_variable"]:metID,
   4.144     [("#Given" ,["functionOf f_f","boundVariable v_v","equalities eqs"]),
   4.145 -    ("#Find"  ,["functionEq f_1_"])
   4.146 +    ("#Find"  ,["functionEq f_1"])
   4.147      ],
   4.148     {rew_ord'="tless_true",rls'=eval_rls,srls=list_rls,prls=e_rls,
   4.149      calc=[], crls = eval_rls, nrls=norm_Rational(*,asm_rls=[],asm_thm=[]*)},
   4.150    "Script Make_fun_by_new_variable (f_f::real) (v_v::real)                " ^
   4.151    "      (eqs::bool list) =                                            " ^
   4.152 -  "(let h_ = (hd o (filterVar f_)) eqs;                                " ^
   4.153 -  "     es_ = dropWhile (ident h_) eqs;                                " ^
   4.154 -  "     vs_ = dropWhile (ident f_) (Vars h_);                           " ^
   4.155 -  "     v_1 = nth_ 1 vs_;                                               " ^
   4.156 -  "     v_2 = nth_ 2 vs_;                                               " ^
   4.157 -  "     e_1 = (hd o (filterVar v_1)) es_;                               " ^
   4.158 -  "     e_2 = (hd o (filterVar v_2)) es_;                               " ^
   4.159 +  "(let h_h = (hd o (filterVar f_f)) eqs;                                " ^
   4.160 +  "     e_s = dropWhile (ident h_h) eqs;                                " ^
   4.161 +  "     v_s = dropWhile (ident f_f) (Vars h_h);                           " ^
   4.162 +  "     v_1 = NTH 1 v_s;                                               " ^
   4.163 +  "     v_2 = NTH 2 v_s;                                               " ^
   4.164 +  "     e_1 = (hd o (filterVar v_1)) e_s;                               " ^
   4.165 +  "     e_2 = (hd o (filterVar v_2)) e_s;                               " ^
   4.166    "  (s_1::bool list) =                                                 " ^
   4.167 -  "                (SubProblem (DiffApp_,[univariate,equation],[no_met])" ^
   4.168 +  "                (SubProblem (DiffApp',[univariate,equation],[no_met])" ^
   4.169    "                    [BOOL e_1, REAL v_1]);                         " ^
   4.170    "  (s_2::bool list) =                                                 " ^
   4.171 -  "                (SubProblem (DiffApp_,[univariate,equation],[no_met])" ^
   4.172 +  "                (SubProblem (DiffApp',[univariate,equation],[no_met])" ^
   4.173    "                    [BOOL e_2, REAL v_2])" ^
   4.174 -  "in Substitute [(v_1 = (rhs o hd) s_1),(v_2 = (rhs o hd) s_2)] h_)"
   4.175 +  "in Substitute [(v_1 = (rhs o hd) s_1),(v_2 = (rhs o hd) s_2)] h_h)"
   4.176  ));
   4.177 +*}
   4.178 +ML{*
   4.179  store_met
   4.180  (prep_met thy "met_diffapp_funexp" [] e_metID
   4.181  (["DiffApp","make_fun_by_explicit"]:metID,
   4.182     [("#Given" ,["functionOf f_f","boundVariable v_v","equalities eqs"]),
   4.183 -    ("#Find"  ,["functionEq f_1_"])
   4.184 +    ("#Find"  ,["functionEq f_1"])
   4.185      ],
   4.186     {rew_ord'="tless_true",rls'=eval_rls,calc=[],srls=list_rls,prls=e_rls,
   4.187      crls = eval_rls, nrls=norm_Rational
   4.188      (*, asm_rls=[],asm_thm=[]*)},
   4.189     "Script Make_fun_by_explicit (f_f::real) (v_v::real)                 " ^
   4.190     "      (eqs::bool list) =                                         " ^
   4.191 -   " (let h_ = (hd o (filterVar f_)) eqs;                            " ^
   4.192 -   "      e_1 = hd (dropWhile (ident h_) eqs);                       " ^
   4.193 -   "      vs_ = dropWhile (ident f_) (Vars h_);                       " ^
   4.194 -   "      v_1 = hd (dropWhile (ident v_v) vs_);                        " ^
   4.195 +   " (let h_h = (hd o (filterVar f_f)) eqs;                            " ^
   4.196 +   "      e_1 = hd (dropWhile (ident h_h) eqs);                       " ^
   4.197 +   "      v_s = dropWhile (ident f_f) (Vars h_h);                       " ^
   4.198 +   "      v_1 = hd (dropWhile (ident v_v) v_s);                        " ^
   4.199     "      (s_1::bool list)=                                           " ^ 
   4.200 -   "              (SubProblem(DiffApp_,[univariate,equation],[no_met])" ^
   4.201 +   "              (SubProblem(DiffApp',[univariate,equation],[no_met])" ^
   4.202     "                          [BOOL e_1, REAL v_1])                 " ^
   4.203 -   " in Substitute [(v_1 = (rhs o hd) s_1)] h_)                       "
   4.204 +   " in Substitute [(v_1 = (rhs o hd) s_1)] h_h)                       "
   4.205     ));
   4.206 +*}
   4.207 +ML{*
   4.208  store_met
   4.209   (prep_met thy "met_diffapp_max_oninterval" [] e_metID
   4.210   (["DiffApp","max_on_interval_by_calculus"]:metID,
   4.211 -   [("#Given" ,["functionEq t_","boundVariable v_v","interval itv_"(*,
   4.212 -		"errorBound err_"*)]),
   4.213 -    ("#Find"  ,["maxArgument v_0_"])
   4.214 +   [("#Given" ,["functionEq t_t","boundVariable v_v","interval i_tv"(*,
   4.215 +		"errorBound e_rr"*)]),
   4.216 +    ("#Find"  ,["maxArgument v_0"])
   4.217      ],
   4.218     {rew_ord'="tless_true",rls'=eval_rls,calc=[],srls = e_rls,prls=e_rls,
   4.219      crls = eval_rls, nrls=norm_Rational
   4.220      (*, asm_rls=[],asm_thm=[]*)},
   4.221     "empty_script"
   4.222     ));
   4.223 +*}
   4.224 +ML{*
   4.225  store_met
   4.226   (prep_met thy "met_diffapp_findvals" [] e_metID
   4.227   (["DiffApp","find_values"]:metID,
     5.1 --- a/src/Tools/isac/Knowledge/EqSystem.thy	Wed Sep 08 17:20:03 2010 +0200
     5.2 +++ b/src/Tools/isac/Knowledge/EqSystem.thy	Wed Sep 08 17:49:36 2010 +0200
     5.3 @@ -415,28 +415,28 @@
     5.4  store_pbt
     5.5   (prep_pbt thy "pbl_equsys" [] e_pblID
     5.6   (["system"],
     5.7 -  [("#Given" ,["equalities es_", "solveForVars vs_"]),
     5.8 +  [("#Given" ,["equalities es_", "solveForVars v_s"]),
     5.9     ("#Find"  ,["solution ss___"](*___ is copy-named*))
    5.10    ],
    5.11    append_rls "e_rls" e_rls [(*for preds in where_*)], 
    5.12 -  SOME "solveSystem es_ vs_", 
    5.13 +  SOME "solveSystem es_ v_s", 
    5.14    []));
    5.15  store_pbt
    5.16   (prep_pbt thy "pbl_equsys_lin" [] e_pblID
    5.17   (["linear", "system"],
    5.18 -  [("#Given" ,["equalities es_", "solveForVars vs_"]),
    5.19 +  [("#Given" ,["equalities es_", "solveForVars v_s"]),
    5.20     (*TODO.WN050929 check linearity*)
    5.21     ("#Find"  ,["solution ss___"])
    5.22    ],
    5.23    append_rls "e_rls" e_rls [(*for preds in where_*)], 
    5.24 -  SOME "solveSystem es_ vs_", 
    5.25 +  SOME "solveSystem es_ v_s", 
    5.26    []));
    5.27  store_pbt
    5.28   (prep_pbt thy "pbl_equsys_lin_2x2" [] e_pblID
    5.29   (["2x2", "linear", "system"],
    5.30    (*~~~~~~~~~~~~~~~~~~~~~~~~~*)
    5.31 -  [("#Given" ,["equalities es_", "solveForVars vs_"]),
    5.32 -   ("#Where"  ,["length_ (es_:: bool list) = 2", "length_ vs_ = 2"]),
    5.33 +  [("#Given" ,["equalities es_", "solveForVars v_s"]),
    5.34 +   ("#Where"  ,["length_ (es_:: bool list) = 2", "length_ v_s = 2"]),
    5.35     ("#Find"  ,["solution ss___"])
    5.36    ],
    5.37    append_rls "prls_2x2_linear_system" e_rls 
    5.38 @@ -445,35 +445,35 @@
    5.39  			      Calc ("op +", eval_binop "#add_"),
    5.40  			      Calc ("op =",eval_equal "#equal_")
    5.41  			      ], 
    5.42 -  SOME "solveSystem es_ vs_", 
    5.43 +  SOME "solveSystem es_ v_s", 
    5.44    []));
    5.45  store_pbt
    5.46   (prep_pbt thy "pbl_equsys_lin_2x2_tri" [] e_pblID
    5.47   (["triangular", "2x2", "linear", "system"],
    5.48 -  [("#Given" ,["equalities es_", "solveForVars vs_"]),
    5.49 +  [("#Given" ,["equalities es_", "solveForVars v_s"]),
    5.50     ("#Where"  ,
    5.51 -    ["(tl vs_) from_ vs_ occur_exactly_in (nth_ 1 (es_::bool list))",
    5.52 -     "    vs_  from_ vs_ occur_exactly_in (nth_ 2 (es_::bool list))"]),
    5.53 +    ["(tl v_s) from_ v_s occur_exactly_in (nth_ 1 (es_::bool list))",
    5.54 +     "    v_s  from_ v_s occur_exactly_in (nth_ 2 (es_::bool list))"]),
    5.55     ("#Find"  ,["solution ss___"])
    5.56    ],
    5.57    prls_triangular, 
    5.58 -  SOME "solveSystem es_ vs_", 
    5.59 +  SOME "solveSystem es_ v_s", 
    5.60    [["EqSystem","top_down_substitution","2x2"]]));
    5.61  store_pbt
    5.62   (prep_pbt thy "pbl_equsys_lin_2x2_norm" [] e_pblID
    5.63   (["normalize", "2x2", "linear", "system"],
    5.64 -  [("#Given" ,["equalities es_", "solveForVars vs_"]),
    5.65 +  [("#Given" ,["equalities es_", "solveForVars v_s"]),
    5.66     ("#Find"  ,["solution ss___"])
    5.67    ],
    5.68    append_rls "e_rls" e_rls [(*for preds in where_*)], 
    5.69 -  SOME "solveSystem es_ vs_", 
    5.70 +  SOME "solveSystem es_ v_s", 
    5.71    [["EqSystem","normalize","2x2"]]));
    5.72  store_pbt
    5.73   (prep_pbt thy "pbl_equsys_lin_3x3" [] e_pblID
    5.74   (["3x3", "linear", "system"],
    5.75    (*~~~~~~~~~~~~~~~~~~~~~~~~~*)
    5.76 -  [("#Given" ,["equalities es_", "solveForVars vs_"]),
    5.77 -   ("#Where"  ,["length_ (es_:: bool list) = 3", "length_ vs_ = 3"]),
    5.78 +  [("#Given" ,["equalities es_", "solveForVars v_s"]),
    5.79 +   ("#Where"  ,["length_ (es_:: bool list) = 3", "length_ v_s = 3"]),
    5.80     ("#Find"  ,["solution ss___"])
    5.81    ],
    5.82    append_rls "prls_3x3_linear_system" e_rls 
    5.83 @@ -482,14 +482,14 @@
    5.84  			      Calc ("op +", eval_binop "#add_"),
    5.85  			      Calc ("op =",eval_equal "#equal_")
    5.86  			      ], 
    5.87 -  SOME "solveSystem es_ vs_", 
    5.88 +  SOME "solveSystem es_ v_s", 
    5.89    []));
    5.90  store_pbt
    5.91   (prep_pbt thy "pbl_equsys_lin_4x4" [] e_pblID
    5.92   (["4x4", "linear", "system"],
    5.93    (*~~~~~~~~~~~~~~~~~~~~~~~~~*)
    5.94 -  [("#Given" ,["equalities es_", "solveForVars vs_"]),
    5.95 -   ("#Where"  ,["length_ (es_:: bool list) = 4", "length_ vs_ = 4"]),
    5.96 +  [("#Given" ,["equalities es_", "solveForVars v_s"]),
    5.97 +   ("#Where"  ,["length_ (es_:: bool list) = 4", "length_ v_s = 4"]),
    5.98     ("#Find"  ,["solution ss___"])
    5.99    ],
   5.100    append_rls "prls_4x4_linear_system" e_rls 
   5.101 @@ -498,34 +498,34 @@
   5.102  			      Calc ("op +", eval_binop "#add_"),
   5.103  			      Calc ("op =",eval_equal "#equal_")
   5.104  			      ], 
   5.105 -  SOME "solveSystem es_ vs_", 
   5.106 +  SOME "solveSystem es_ v_s", 
   5.107    []));
   5.108  store_pbt
   5.109   (prep_pbt thy "pbl_equsys_lin_4x4_tri" [] e_pblID
   5.110   (["triangular", "4x4", "linear", "system"],
   5.111 -  [("#Given" ,["equalities es_", "solveForVars vs_"]),
   5.112 +  [("#Given" ,["equalities es_", "solveForVars v_s"]),
   5.113     ("#Where" , (*accepts missing variables up to diagional form*)
   5.114 -    ["(nth_ 1 (vs_::real list)) occurs_in (nth_ 1 (es_::bool list))",
   5.115 -     "(nth_ 2 (vs_::real list)) occurs_in (nth_ 2 (es_::bool list))",
   5.116 -     "(nth_ 3 (vs_::real list)) occurs_in (nth_ 3 (es_::bool list))",
   5.117 -     "(nth_ 4 (vs_::real list)) occurs_in (nth_ 4 (es_::bool list))"
   5.118 +    ["(nth_ 1 (v_s::real list)) occurs_in (nth_ 1 (es_::bool list))",
   5.119 +     "(nth_ 2 (v_s::real list)) occurs_in (nth_ 2 (es_::bool list))",
   5.120 +     "(nth_ 3 (v_s::real list)) occurs_in (nth_ 3 (es_::bool list))",
   5.121 +     "(nth_ 4 (v_s::real list)) occurs_in (nth_ 4 (es_::bool list))"
   5.122       ]),
   5.123     ("#Find"  ,["solution ss___"])
   5.124    ],
   5.125    append_rls "prls_tri_4x4_lin_sys" prls_triangular
   5.126  	     [Calc ("Atools.occurs'_in",eval_occurs_in "")], 
   5.127 -  SOME "solveSystem es_ vs_", 
   5.128 +  SOME "solveSystem es_ v_s", 
   5.129    [["EqSystem","top_down_substitution","4x4"]]));
   5.130  
   5.131  store_pbt
   5.132   (prep_pbt thy "pbl_equsys_lin_4x4_norm" [] e_pblID
   5.133   (["normalize", "4x4", "linear", "system"],
   5.134 -  [("#Given" ,["equalities es_", "solveForVars vs_"]),
   5.135 +  [("#Given" ,["equalities es_", "solveForVars v_s"]),
   5.136     (*length_ is checked 1 level above*)
   5.137     ("#Find"  ,["solution ss___"])
   5.138    ],
   5.139    append_rls "e_rls" e_rls [(*for preds in where_*)], 
   5.140 -  SOME "solveSystem es_ vs_", 
   5.141 +  SOME "solveSystem es_ v_s", 
   5.142    [["EqSystem","normalize","4x4"]]));
   5.143  
   5.144  
   5.145 @@ -553,10 +553,10 @@
   5.146  store_met
   5.147      (prep_met thy "met_eqsys_topdown_2x2" [] e_metID
   5.148  	 (["EqSystem","top_down_substitution","2x2"],
   5.149 -	  [("#Given" ,["equalities es_", "solveForVars vs_"]),
   5.150 +	  [("#Given" ,["equalities es_", "solveForVars v_s"]),
   5.151  	   ("#Where"  ,
   5.152 -	    ["(tl vs_) from_ vs_ occur_exactly_in (nth_ 1 (es_::bool list))",
   5.153 -	     "    vs_  from_ vs_ occur_exactly_in (nth_ 2 (es_::bool list))"]),
   5.154 +	    ["(tl v_s) from_ v_s occur_exactly_in (nth_ 1 (es_::bool list))",
   5.155 +	     "    v_s  from_ v_s occur_exactly_in (nth_ 2 (es_::bool list))"]),
   5.156  	   ("#Find"  ,["solution ss___"])
   5.157  	   ],
   5.158  	  {rew_ord'="ord_simplify_System", rls' = Erls, calc = [], 
   5.159 @@ -566,19 +566,19 @@
   5.160  				   Thm ("tl_Nil",num_str @{thm tl_Nil})
   5.161  				   ], 
   5.162  	   prls = prls_triangular, crls = Erls, nrls = Erls},
   5.163 -"Script SolveSystemScript (es_::bool list) (vs_::real list) =                " ^
   5.164 +"Script SolveSystemScript (es_::bool list) (v_s::real list) =                " ^
   5.165  "  (let e1__ = Take (hd es_);                                                " ^
   5.166 -"       e1__ = ((Try (Rewrite_Set_Inst [(bdv_1, hd vs_),(bdv_2, hd (tl vs_))]" ^
   5.167 +"       e1__ = ((Try (Rewrite_Set_Inst [(bdv_1, hd v_s),(bdv_2, hd (tl v_s))]" ^
   5.168  "                                  isolate_bdvs False))     @@               " ^
   5.169 -"               (Try (Rewrite_Set_Inst [(bdv_1, hd vs_),(bdv_2, hd (tl vs_))]" ^
   5.170 +"               (Try (Rewrite_Set_Inst [(bdv_1, hd v_s),(bdv_2, hd (tl v_s))]" ^
   5.171  "                                  simplify_System False))) e1__;            " ^
   5.172  "       e2__ = Take (hd (tl es_));                                           " ^
   5.173  "       e2__ = ((Substitute [e1__]) @@                                       " ^
   5.174 -"               (Try (Rewrite_Set_Inst [(bdv_1, hd vs_),(bdv_2, hd (tl vs_))]" ^
   5.175 +"               (Try (Rewrite_Set_Inst [(bdv_1, hd v_s),(bdv_2, hd (tl v_s))]" ^
   5.176  "                                  simplify_System_parenthesized False)) @@  " ^
   5.177 -"               (Try (Rewrite_Set_Inst [(bdv_1, hd vs_),(bdv_2, hd (tl vs_))]" ^
   5.178 +"               (Try (Rewrite_Set_Inst [(bdv_1, hd v_s),(bdv_2, hd (tl v_s))]" ^
   5.179  "                                  isolate_bdvs False))     @@               " ^
   5.180 -"               (Try (Rewrite_Set_Inst [(bdv_1, hd vs_),(bdv_2, hd (tl vs_))]" ^
   5.181 +"               (Try (Rewrite_Set_Inst [(bdv_1, hd v_s),(bdv_2, hd (tl v_s))]" ^
   5.182  "                                  simplify_System False))) e2__;            " ^
   5.183  "       es__ = Take [e1__, e2__]                                             " ^
   5.184  "   in (Try (Rewrite_Set order_system False)) es__)"
   5.185 @@ -587,16 +587,16 @@
   5.186    but it does not yet work due to preliminary script-interpreter,
   5.187    see eqsystem.sml 'script [EqSystem,top_down_substitution,2x2] Vers.2'
   5.188  
   5.189 -"Script SolveSystemScript (es_::bool list) (vs_::real list) =         " ^
   5.190 +"Script SolveSystemScript (es_::bool list) (v_s::real list) =         " ^
   5.191  "  (let es__ = Take es_;                                              " ^
   5.192  "       e1__ = hd es__;                                               " ^
   5.193  "       e2__ = hd (tl es__);                                          " ^
   5.194  "       es__ = [e1__, Substitute [e1__] e2__]                         " ^
   5.195 -"   in ((Try (Rewrite_Set_Inst [(bdv_1, hd vs_),(bdv_2, hd (tl vs_))]" ^
   5.196 +"   in ((Try (Rewrite_Set_Inst [(bdv_1, hd v_s),(bdv_2, hd (tl v_s))]" ^
   5.197  "                                  simplify_System_parenthesized False)) @@ " ^
   5.198 -"       (Try (Rewrite_Set_Inst [(bdv_1, hd vs_),(bdv_2, hd (tl vs_))] " ^
   5.199 +"       (Try (Rewrite_Set_Inst [(bdv_1, hd v_s),(bdv_2, hd (tl v_s))] " ^
   5.200  "                              isolate_bdvs False))              @@   " ^
   5.201 -"       (Try (Rewrite_Set_Inst [(bdv_1, hd vs_),(bdv_2, hd (tl vs_))]" ^
   5.202 +"       (Try (Rewrite_Set_Inst [(bdv_1, hd v_s),(bdv_2, hd (tl v_s))]" ^
   5.203  "                                  simplify_System False))) es__)"
   5.204  ---------------------------------------------------------------------------*)
   5.205  	  ));
   5.206 @@ -611,7 +611,7 @@
   5.207  store_met
   5.208      (prep_met thy "met_eqsys_norm_2x2" [] e_metID
   5.209  	      (["EqSystem","normalize","2x2"],
   5.210 -	       [("#Given" ,["equalities es_", "solveForVars vs_"]),
   5.211 +	       [("#Given" ,["equalities es_", "solveForVars v_s"]),
   5.212  		("#Find"  ,["solution ss___"])],
   5.213  	       {rew_ord'="tless_true", rls' = Erls, calc = [], 
   5.214  		srls = append_rls "srls_normalize_2x2" e_rls
   5.215 @@ -620,17 +620,17 @@
   5.216  				   Thm ("tl_Nil",num_str @{thm tl_Nil})
   5.217  				   ], 
   5.218  		prls = Erls, crls = Erls, nrls = Erls},
   5.219 -"Script SolveSystemScript (es_::bool list) (vs_::real list) =                " ^
   5.220 +"Script SolveSystemScript (es_::bool list) (v_s::real list) =                " ^
   5.221  "  (let es__ = ((Try (Rewrite_Set norm_Rational False)) @@                   " ^
   5.222 -"               (Try (Rewrite_Set_Inst [(bdv_1, hd vs_),(bdv_2, hd (tl vs_))]" ^
   5.223 +"               (Try (Rewrite_Set_Inst [(bdv_1, hd v_s),(bdv_2, hd (tl v_s))]" ^
   5.224  "                                  simplify_System_parenthesized False)) @@  " ^
   5.225 -"               (Try (Rewrite_Set_Inst [(bdv_1, hd vs_),(bdv_2, hd (tl vs_))]" ^
   5.226 +"               (Try (Rewrite_Set_Inst [(bdv_1, hd v_s),(bdv_2, hd (tl v_s))]" ^
   5.227  "                                                    isolate_bdvs False)) @@ " ^
   5.228 -"               (Try (Rewrite_Set_Inst [(bdv_1, hd vs_),(bdv_2, hd (tl vs_))]" ^
   5.229 +"               (Try (Rewrite_Set_Inst [(bdv_1, hd v_s),(bdv_2, hd (tl v_s))]" ^
   5.230  "                                  simplify_System_parenthesized False)) @@  " ^
   5.231  "               (Try (Rewrite_Set order_system False))) es_                  " ^
   5.232  "   in (SubProblem (EqSystem_,[linear,system],[no_met])                      " ^
   5.233 -"                  [BOOL_LIST es__, REAL_LIST vs_]))"
   5.234 +"                  [BOOL_LIST es__, REAL_LIST v_s]))"
   5.235  	       ));
   5.236  
   5.237  (*this is for nth_ only*)
   5.238 @@ -651,7 +651,7 @@
   5.239  store_met
   5.240      (prep_met thy "met_eqsys_norm_4x4" [] e_metID
   5.241  	      (["EqSystem","normalize","4x4"],
   5.242 -	       [("#Given" ,["equalities es_", "solveForVars vs_"]),
   5.243 +	       [("#Given" ,["equalities es_", "solveForVars v_s"]),
   5.244  		("#Find"  ,["solution ss___"])],
   5.245  	       {rew_ord'="tless_true", rls' = Erls, calc = [], 
   5.246  		srls = append_rls "srls_normalize_4x4" srls
   5.247 @@ -661,32 +661,32 @@
   5.248  				   ], 
   5.249  		prls = Erls, crls = Erls, nrls = Erls},
   5.250  (*GOON met ["EqSystem","normalize","4x4"] @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@*)
   5.251 -"Script SolveSystemScript (es_::bool list) (vs_::real list) =                " ^
   5.252 +"Script SolveSystemScript (es_::bool list) (v_s::real list) =                " ^
   5.253  "  (let es__ =                                                               " ^
   5.254  "     ((Try (Rewrite_Set norm_Rational False)) @@                            " ^
   5.255  "      (Repeat (Rewrite commute_0_equality False)) @@                        " ^
   5.256 -"      (Try (Rewrite_Set_Inst [(bdv_1, nth_ 1 vs_),(bdv_2, nth_ 2 vs_ ),     " ^
   5.257 -"                              (bdv_3, nth_ 3 vs_),(bdv_3, nth_ 4 vs_ )]     " ^
   5.258 +"      (Try (Rewrite_Set_Inst [(bdv_1, nth_ 1 v_s),(bdv_2, nth_ 2 v_s ),     " ^
   5.259 +"                              (bdv_3, nth_ 3 v_s),(bdv_3, nth_ 4 v_s )]     " ^
   5.260  "                             simplify_System_parenthesized False))    @@    " ^
   5.261 -"      (Try (Rewrite_Set_Inst [(bdv_1, nth_ 1 vs_),(bdv_2, nth_ 2 vs_ ),     " ^
   5.262 -"                              (bdv_3, nth_ 3 vs_),(bdv_3, nth_ 4 vs_ )]     " ^
   5.263 +"      (Try (Rewrite_Set_Inst [(bdv_1, nth_ 1 v_s),(bdv_2, nth_ 2 v_s ),     " ^
   5.264 +"                              (bdv_3, nth_ 3 v_s),(bdv_3, nth_ 4 v_s )]     " ^
   5.265  "                             isolate_bdvs_4x4 False))                 @@    " ^
   5.266 -"      (Try (Rewrite_Set_Inst [(bdv_1, nth_ 1 vs_),(bdv_2, nth_ 2 vs_ ),     " ^
   5.267 -"                              (bdv_3, nth_ 3 vs_),(bdv_3, nth_ 4 vs_ )]     " ^
   5.268 +"      (Try (Rewrite_Set_Inst [(bdv_1, nth_ 1 v_s),(bdv_2, nth_ 2 v_s ),     " ^
   5.269 +"                              (bdv_3, nth_ 3 v_s),(bdv_3, nth_ 4 v_s )]     " ^
   5.270  "                             simplify_System_parenthesized False))    @@    " ^
   5.271  "      (Try (Rewrite_Set order_system False)))                           es_ " ^
   5.272  "   in (SubProblem (EqSystem_,[linear,system],[no_met])                      " ^
   5.273 -"                  [BOOL_LIST es__, REAL_LIST vs_]))"
   5.274 +"                  [BOOL_LIST es__, REAL_LIST v_s]))"
   5.275  ));
   5.276  store_met
   5.277  (prep_met thy "met_eqsys_topdown_4x4" [] e_metID
   5.278  	  (["EqSystem","top_down_substitution","4x4"],
   5.279 -	   [("#Given" ,["equalities es_", "solveForVars vs_"]),
   5.280 +	   [("#Given" ,["equalities es_", "solveForVars v_s"]),
   5.281  	    ("#Where" , (*accepts missing variables up to diagonal form*)
   5.282 -	     ["(nth_ 1 (vs_::real list)) occurs_in (nth_ 1 (es_::bool list))",
   5.283 -	      "(nth_ 2 (vs_::real list)) occurs_in (nth_ 2 (es_::bool list))",
   5.284 -	      "(nth_ 3 (vs_::real list)) occurs_in (nth_ 3 (es_::bool list))",
   5.285 -	      "(nth_ 4 (vs_::real list)) occurs_in (nth_ 4 (es_::bool list))"
   5.286 +	     ["(nth_ 1 (v_s::real list)) occurs_in (nth_ 1 (es_::bool list))",
   5.287 +	      "(nth_ 2 (v_s::real list)) occurs_in (nth_ 2 (es_::bool list))",
   5.288 +	      "(nth_ 3 (v_s::real list)) occurs_in (nth_ 3 (es_::bool list))",
   5.289 +	      "(nth_ 4 (v_s::real list)) occurs_in (nth_ 4 (es_::bool list))"
   5.290  	      ]),
   5.291  	    ("#Find"  ,["solution ss___"])
   5.292  	    ],
   5.293 @@ -696,18 +696,18 @@
   5.294  			      [Calc ("Atools.occurs'_in",eval_occurs_in "")], 
   5.295  	    crls = Erls, nrls = Erls},
   5.296  (*FIXXXXME.WN060916: this script works ONLY for exp 7.79 @@@@@@@@@@@@@@@@@@@@*)
   5.297 -"Script SolveSystemScript (es_::bool list) (vs_::real list) =                " ^
   5.298 +"Script SolveSystemScript (es_::bool list) (v_s::real list) =                " ^
   5.299  "  (let e1_ = nth_ 1 es_;                                                    " ^
   5.300  "       e2_ = Take (nth_ 2 es_);                                             " ^
   5.301  "       e2_ = ((Substitute [e1_]) @@                                         " ^
   5.302 -"              (Try (Rewrite_Set_Inst [(bdv_1,nth_ 1 vs_),(bdv_2,nth_ 2 vs_)," ^
   5.303 -"                                      (bdv_3,nth_ 3 vs_),(bdv_4,nth_ 4 vs_)]" ^
   5.304 +"              (Try (Rewrite_Set_Inst [(bdv_1,nth_ 1 v_s),(bdv_2,nth_ 2 v_s)," ^
   5.305 +"                                      (bdv_3,nth_ 3 v_s),(bdv_4,nth_ 4 v_s)]" ^
   5.306  "                                 simplify_System_parenthesized False)) @@   " ^
   5.307 -"              (Try (Rewrite_Set_Inst [(bdv_1,nth_ 1 vs_),(bdv_2,nth_ 2 vs_)," ^
   5.308 -"                                      (bdv_3,nth_ 3 vs_),(bdv_4,nth_ 4 vs_)]" ^
   5.309 +"              (Try (Rewrite_Set_Inst [(bdv_1,nth_ 1 v_s),(bdv_2,nth_ 2 v_s)," ^
   5.310 +"                                      (bdv_3,nth_ 3 v_s),(bdv_4,nth_ 4 v_s)]" ^
   5.311  "                                 isolate_bdvs False))                  @@   " ^
   5.312 -"              (Try (Rewrite_Set_Inst [(bdv_1,nth_ 1 vs_),(bdv_2,nth_ 2 vs_)," ^
   5.313 -"                                      (bdv_3,nth_ 3 vs_),(bdv_4,nth_ 4 vs_)]" ^
   5.314 +"              (Try (Rewrite_Set_Inst [(bdv_1,nth_ 1 v_s),(bdv_2,nth_ 2 v_s)," ^
   5.315 +"                                      (bdv_3,nth_ 3 v_s),(bdv_4,nth_ 4 v_s)]" ^
   5.316  "                                 norm_Rational False)))             e2_     " ^
   5.317  "    in [e1_, e2_, nth_ 3 es_, nth_ 4 es_])"
   5.318  ));
     6.1 --- a/test/Tools/isac/Knowledge/diffapp.sml	Wed Sep 08 17:20:03 2010 +0200
     6.2 +++ b/test/Tools/isac/Knowledge/diffapp.sml	Wed Sep 08 17:49:36 2010 +0200
     6.3 @@ -28,7 +28,7 @@
     6.4  " #################################################### ";
     6.5  " -------------- [maximum_of,function] --------------- ";
     6.6  val pbt = 
     6.7 -    ["fixedValues fix_","maximum m_","valuesFor vs_","relations rs_"];
     6.8 +    ["fixedValues f_ix","maximum m_","valuesFor v_s","relations r_s"];
     6.9  map (the o (parseold thy)) pbt;
    6.10  val fmz =
    6.11      ["fixedValues [r=Arbfix]","maximum A",
    6.12 @@ -69,7 +69,7 @@
    6.13  " ---- [on_interval,maximum_of,function] ---- ";
    6.14  val pbt = 
    6.15      ["functionTerm t_","boundVariable v_v","interval itv_",
    6.16 -     "errorBound err_","maxArgument v_0_"];
    6.17 +     "errorBound err_","maxArgument v_0"];
    6.18  map (the o (parseold thy)) pbt;
    6.19  val fmz12 =
    6.20      [(*28.11.00: "functionTerm (A_0 = a*sqrt(#4*r^^^#2 - a^^^#2))",*)
    6.21 @@ -100,7 +100,7 @@
    6.22  " --------- [find_values,tool] --------- ";
    6.23  val pbt = 
    6.24      ["maxArgument ma_","functionTerm f_f","boundVariable v_v",
    6.25 -     "valuesFor vls_","additionalRels rs_"];
    6.26 +     "valuesFor vls_","additionalRels r_s"];
    6.27  map (the o (parseold thy)) pbt;
    6.28  val fmz1 =
    6.29      ["maxArgument (a_0=(srqt 2)*r)",
    6.30 @@ -428,12 +428,12 @@
    6.31   val mits = get_obj g_met pt (fst p);
    6.32   writeln (itms2str_ ctxt mits);
    6.33  (*
    6.34 - if itms2str_ ctxt mits = "[\n(1 ,[1] ,true ,#Given ,Cor functionEq (hd rs_) ,(t_, [hd rs_])),\n(2 ,[1] ,true ,#Given ,Cor boundVariable v_v ,(v_, [v_])),\n(3 ,[1] ,true ,#Given ,Cor interval itv_ ,(itv_, [itv_])),\n(4 ,[1] ,true ,#Find ,Cor maxArgument v__0 ,(v_0_, [v__0]))]" then ()
    6.35 + if itms2str_ ctxt mits = "[\n(1 ,[1] ,true ,#Given ,Cor functionEq (hd r_s) ,(t_, [hd r_s])),\n(2 ,[1] ,true ,#Given ,Cor boundVariable v_v ,(v_, [v_])),\n(3 ,[1] ,true ,#Given ,Cor interval itv_ ,(itv_, [itv_])),\n(4 ,[1] ,true ,#Find ,Cor maxArgument v__0 ,(v_0, [v__0]))]" then ()
    6.36   else raise error "diffapp.sml: diff.behav. in autoCalc .. scripts for max 1";
    6.37  *)
    6.38   (*FIXME: the environments contain identifers, and NOT values ?!?!?*)
    6.39  (* WN051209 while extending 'fun step' for initac, this became better ...
    6.40 - if itms2str_ ctxt mits = "[\n(1 ,[1,2,3] ,true ,#Given ,Cor fixedValues [r = Arbfix] ,(fix_, [[r = Arbfix]])),\n(2 ,[1,2,3] ,true ,#Find ,Cor maximum A ,(m_, [A])),\n(3 ,[1,2,3] ,true ,#Find ,Cor valuesFor [a, b] ,(vs_, [[a],[b]])),\n(4 ,[1,2] ,true ,#Relate ,Cor relations [A = a * b, (a / 2) ^^^ 2 + (b / 2) ^^^ 2 = r ^^^ 2] ,(rs_, [[A = a * b],[(a / 2) ^^^ 2 + (b / 2) ^^^ 2 = r ^^^ 2]])),\n(6 ,[1] ,true ,#undef ,Cor boundVariable a ,(v_, [a])),\n(9 ,[1,2] ,true ,#undef ,Cor interval {x. 0 <= x & x <= 2 * r} ,(itv_, [{x. 0 <= x & x <= 2 * r}])),\n(11 ,[1,2,3] ,true ,#undef ,Cor errorBound (eps = 0) ,(err_, [eps = 0]))]" then ()
    6.41 + if itms2str_ ctxt mits = "[\n(1 ,[1,2,3] ,true ,#Given ,Cor fixedValues [r = Arbfix] ,(f_ix, [[r = Arbfix]])),\n(2 ,[1,2,3] ,true ,#Find ,Cor maximum A ,(m_, [A])),\n(3 ,[1,2,3] ,true ,#Find ,Cor valuesFor [a, b] ,(v_s, [[a],[b]])),\n(4 ,[1,2] ,true ,#Relate ,Cor relations [A = a * b, (a / 2) ^^^ 2 + (b / 2) ^^^ 2 = r ^^^ 2] ,(r_s, [[A = a * b],[(a / 2) ^^^ 2 + (b / 2) ^^^ 2 = r ^^^ 2]])),\n(6 ,[1] ,true ,#undef ,Cor boundVariable a ,(v_, [a])),\n(9 ,[1,2] ,true ,#undef ,Cor interval {x. 0 <= x & x <= 2 * r} ,(itv_, [{x. 0 <= x & x <= 2 * r}])),\n(11 ,[1,2,3] ,true ,#undef ,Cor errorBound (eps = 0) ,(err_, [eps = 0]))]" then ()
    6.42   else raise error "diffapp.sml: diff.behav. in autoCalc .. scripts for max 1";
    6.43  *)
    6.44  
    6.45 @@ -443,25 +443,25 @@
    6.46  "--------------------- 30.4.03: maximum .. rewrite_set_ list_rls ---------";
    6.47  "--------------------- 30.4.03: maximum .. rewrite_set_ list_rls ---------";
    6.48  str2term
    6.49 -  "Script Maximum_value(fix_::bool list)(m_::real) (rs_::bool list)\
    6.50 +  "Script Maximum_value(f_ix::bool list)(m_::real) (r_s::bool list)\
    6.51     \      (v_v::real) (itv_v::real set) (err_::bool) =          \ 
    6.52 -   \ (let e_e = (hd o (filterVar m_)) rs_;              \
    6.53 -   \      t_ = (if 1 < length_ rs_                            \
    6.54 +   \ (let e_e = (hd o (filterVar m_)) r_s;              \
    6.55 +   \      t_ = (if 1 < length_ r_s                            \
    6.56     \           then (SubProblem (Reals_,[make,function],[no_met])\
    6.57 -   \                     [REAL m_, REAL v_v, BOOL_LIST rs_])\
    6.58 -   \           else (hd rs_));                                \
    6.59 +   \                     [REAL m_, REAL v_v, BOOL_LIST r_s])\
    6.60 +   \           else (hd r_s));                                \
    6.61     \      (mx_::real) = SubProblem (Reals_,[on_interval,max_of,function], \
    6.62     \                                [Isac,maximum_on_interval])\
    6.63     \                               [BOOL t_, REAL v_v, REAL_SET itv_]\
    6.64     \ in ((SubProblem (Reals_,[find_values,tool],[Isac,find_values])   \
    6.65     \      [REAL mx_, REAL (Rhs t_), REAL v_v, REAL m_,     \
    6.66 -   \       BOOL_LIST (dropWhile (ident e_e) rs_)])::bool list))";
    6.67 +   \       BOOL_LIST (dropWhile (ident e_e) r_s)])::bool list))";
    6.68  
    6.69 -val fix_ = (str2term "fix_::bool list", 
    6.70 +val f_ix = (str2term "f_ix::bool list", 
    6.71  	    str2term "[r=Arbfix]");
    6.72  val m_   = (str2term "m_::real", 
    6.73  	    str2term "A");
    6.74 -val rs_  = (str2term "rs_::bool list", 
    6.75 +val r_s  = (str2term "rs_::bool list", 
    6.76  	    str2term "[A = a*b, (a/2)^^^2 + (b/2)^^^2 = r^^^2]");
    6.77  val v_v   = (str2term "v_v::real", 
    6.78  	    str2term "b");
    6.79 @@ -469,10 +469,10 @@
    6.80  	    str2term "{x::real. 0 <= x & x <= 2*r}");
    6.81  val err_ = (str2term "err_::bool", 
    6.82  	    str2term "eps=0");
    6.83 -val env = [fix_, m_, rs_ ,v_, itv_, err_];
    6.84 +val env = [f_ix, m_, r_s ,v_, itv_, err_];
    6.85  
    6.86  (*--- 1.line in script ---*)
    6.87 -val t = str2term "(hd o (filterVar m_)) (rs_::bool list)";
    6.88 +val t = str2term "(hd o (filterVar m_)) (r_s::bool list)";
    6.89  val s = subst_atomic env t;
    6.90  term2str s;
    6.91  "(hd o filterVar A) [A = a * b, (a / 2) ^^^ 2 + (b / 2) ^^^ 2 = r ^^^ 2]";
    6.92 @@ -482,7 +482,7 @@
    6.93  val env = env @ [(str2term "e_::bool",str2term "A = a * b")];
    6.94  
    6.95  (*--- 2.line: condition alone ---*)
    6.96 -val t = str2term "1 < length_ (rs_::bool list)";
    6.97 +val t = str2term "1 < length_ (r_s::bool list)";
    6.98  val s = subst_atomic env t;
    6.99  term2str s;
   6.100  "1 < length_ [A = a * b, (a / 2) ^^^ 2 + (b / 2) ^^^ 2 = r ^^^ 2]";
   6.101 @@ -492,10 +492,10 @@
   6.102  
   6.103  (*--- 2.line in script ---*)
   6.104  val t = str2term 
   6.105 -	    "(if 1 < length_ rs_                            \
   6.106 +	    "(if 1 < length_ r_s                            \
   6.107     \           then (SubProblem (Reals_,[make,function],[no_met])\
   6.108 -   \                     [REAL m_, REAL v_v, BOOL_LIST rs_])\
   6.109 -   \           else (hd rs_))";
   6.110 +   \                     [REAL m_, REAL v_v, BOOL_LIST r_s])\
   6.111 +   \           else (hd r_s))";
   6.112  val s = subst_atomic env t;
   6.113  term2str s;
   6.114  "if 1 < length_ [A = a * b, (a / 2) ^^^ 2 + (b / 2) ^^^ 2 = r ^^^ 2]\
   6.115 @@ -523,8 +523,8 @@
   6.116     \      (eqs::bool list) =                                 \
   6.117     \ (let h_  = (hd o (filterVar f_)) eqs;                   \
   6.118     \      e_1 = hd (dropWhile (ident h_) eqs);               \
   6.119 -   \      vs_ = dropWhile (ident f_) (Vars h_);                \
   6.120 -   \      v_1 = hd (dropWhile (ident v_v) vs_);                \
   6.121 +   \      v_s = dropWhile (ident f_) (Vars h_);                \
   6.122 +   \      v_1 = hd (dropWhile (ident v_v) v_s);                \
   6.123     \      (s_1::bool list)=(SubProblem(Reals_,[univar,equation],[no_met])\
   6.124     \                          [BOOL e_1, REAL v_1])\
   6.125     \ in Substitute [(v_1 = (rhs o hd) s_1)] h_)";
   6.126 @@ -573,7 +573,7 @@
   6.127  val env = env @ [(str2term "vs_::real list", str2term s')];
   6.128  
   6.129  (*--- 4.line in script ---*)
   6.130 -val t = str2term "hd (dropWhile (ident v_v) vs_)";
   6.131 +val t = str2term "hd (dropWhile (ident v_v) v_s)";
   6.132  val s = subst_atomic env t;
   6.133  term2str s;
   6.134  val t = str2term "hd (dropWhile (ident b) [a, b])";
   6.135 @@ -614,9 +614,9 @@
   6.136     \      (eqs::bool list) =                                 \
   6.137     \(let h_ = (hd o (filterVar f_)) eqs;             \
   6.138     \     es_ = dropWhile (ident h_) eqs;                    \
   6.139 -   \     vs_ = dropWhile (ident f_) (Vars h_);                \
   6.140 -   \     v_1 = nth_ 1 vs_;                                   \
   6.141 -   \     v_2 = nth_ 2 vs_;                                   \
   6.142 +   \     v_s = dropWhile (ident f_) (Vars h_);                \
   6.143 +   \     v_1 = nth_ 1 v_s;                                   \
   6.144 +   \     v_2 = nth_ 2 v_s;                                   \
   6.145     \     e_1 = (hd o (filterVar v_1)) es_;            \
   6.146     \     e_2 = (hd o (filterVar v_2)) es_;            \
   6.147     \  (s_1::bool list) = (SubProblem (Reals_,[univar,equation],[no_met])\
   6.148 @@ -669,7 +669,7 @@
   6.149  val env = env @ [(str2term "vs_::real list", str2term s')];
   6.150  
   6.151  (*--- 4.line in script ---*)
   6.152 -val t = str2term "nth_ 1 vs_";
   6.153 +val t = str2term "nth_ 1 v_s";
   6.154  val s = subst_atomic env t;
   6.155  term2str s;
   6.156  val t = str2term "nth_ 1 [a, b]";
   6.157 @@ -679,7 +679,7 @@
   6.158  val env = env @ [(str2term "v_1", str2term s')];
   6.159  
   6.160  (*--- 5.line in script ---*)
   6.161 -val t = str2term "nth_ 2 vs_";
   6.162 +val t = str2term "nth_ 2 v_s";
   6.163  val s = subst_atomic env t;
   6.164  term2str s;
   6.165  val t = str2term "nth_ 2 [a, b]";
     7.1 --- a/test/Tools/isac/Knowledge/eqsystem.sml	Wed Sep 08 17:20:03 2010 +0200
     7.2 +++ b/test/Tools/isac/Knowledge/eqsystem.sml	Wed Sep 08 17:49:36 2010 +0200
     7.3 @@ -101,7 +101,7 @@
     7.4  atomty (term_of t);
     7.5  
     7.6  val t = str2term 
     7.7 -"(tl (tl (tl vs_))) from_ vs_ occur_exactly_in (nth_ 1 (es_::bool list))";
     7.8 +"(tl (tl (tl v_s))) from_ v_s occur_exactly_in (nth_ 1 (es_::bool list))";
     7.9  atomty t;
    7.10  val t = str2term 
    7.11  "(tl (tl (tl [c,c_2,c_3,c_4]))) from_ [c,c_2,c_3,c_4] occur_exactly_in \
    7.12 @@ -284,99 +284,99 @@
    7.13  "----------- script [EqSystem,normalize,2x2] ---------------------";
    7.14  "----------- script [EqSystem,normalize,2x2] ---------------------";
    7.15  val str = 
    7.16 -"Script SolveSystemScript (es_::bool list) (vs_::real list) = \
    7.17 -\  (let es__ = (Rewrite_Set_Inst [(bdv_1, hd vs_),(bdv_2, hd (tl vs_))]\
    7.18 +"Script SolveSystemScript (es_::bool list) (v_s::real list) = \
    7.19 +\  (let es__ = (Rewrite_Set_Inst [(bdv_1, hd v_s),(bdv_2, hd (tl v_s))]\
    7.20  \                                simplify_System_parenthesized False) es_  \
    7.21  \   in ([]))";
    7.22  val sc = ((inst_abs thy) o term_of o the o (parse thy)) str;
    7.23  val str = 
    7.24 -"Script SolveSystemScript (es_::bool list) (vs_::real list) = \
    7.25 -\  (let es__ = (Rewrite_Set_Inst [(bdv_1, hd vs_),(bdv_2, hd (tl vs_))]\
    7.26 +"Script SolveSystemScript (es_::bool list) (v_s::real list) = \
    7.27 +\  (let es__ = (Rewrite_Set_Inst [(bdv_1, hd v_s),(bdv_2, hd (tl v_s))]\
    7.28  \                                 simplify_System_parenthesized False) es_  \
    7.29  \   in (SubProblem (Biegelinie_,[linear,system],[no_met])\
    7.30  \                  []))";
    7.31  val sc = ((inst_abs thy) o term_of o the o (parse thy)) str;
    7.32  val str = 
    7.33 -"Script SolveSystemScript (es_::bool list) (vs_::real list) = \
    7.34 -\  (let es__ = (Rewrite_Set_Inst [(bdv_1, hd vs_),(bdv_2, hd (tl vs_))]\
    7.35 +"Script SolveSystemScript (es_::bool list) (v_s::real list) = \
    7.36 +\  (let es__ = (Rewrite_Set_Inst [(bdv_1, hd v_s),(bdv_2, hd (tl v_s))]\
    7.37  \                                 simplify_System_parenthesized False) es_  \
    7.38  \   in (SubProblem (Biegelinie_,[linear,system],[no_met])\
    7.39 -\                  [BOOL_LIST es__, REAL_LIST vs_]))"
    7.40 +\                  [BOOL_LIST es__, REAL_LIST v_s]))"
    7.41  ;
    7.42  val sc = ((inst_abs thy) o term_of o the o (parse thy)) str;
    7.43  val str = 
    7.44 -"Script SolveSystemScript (es_::bool list) (vs_::real list) = \
    7.45 -\  (let es__ = Try (Rewrite_Set_Inst [(bdv_1, hd vs_),(bdv_2, hd (tl vs_))]\
    7.46 +"Script SolveSystemScript (es_::bool list) (v_s::real list) = \
    7.47 +\  (let es__ = Try (Rewrite_Set_Inst [(bdv_1, hd v_s),(bdv_2, hd (tl v_s))]\
    7.48  \                                 simplify_System_parenthesized False) es_  \
    7.49  \   in (SubProblem (Biegelinie_,[linear,system],[no_met])\
    7.50 -\                  [BOOL_LIST es__, REAL_LIST vs_]))"
    7.51 +\                  [BOOL_LIST es__, REAL_LIST v_s]))"
    7.52  ;
    7.53  val sc = ((inst_abs thy) o term_of o the o (parse thy)) str;
    7.54  val str = 
    7.55 -"Script SolveSystemScript (es_::bool list) (vs_::real list) = \
    7.56 -\  (let es__ = (Try (Rewrite_Set_Inst [(bdv_1, hd vs_),(bdv_2, hd (tl vs_))]\
    7.57 +"Script SolveSystemScript (es_::bool list) (v_s::real list) = \
    7.58 +\  (let es__ = (Try (Rewrite_Set_Inst [(bdv_1, hd v_s),(bdv_2, hd (tl v_s))]\
    7.59  \                                 simplify_System_parenthesized False)) es_  \
    7.60  \   in (SubProblem (Biegelinie_,[linear,system],[no_met])\
    7.61 -\                  [BOOL_LIST es__, REAL_LIST vs_]))"
    7.62 +\                  [BOOL_LIST es__, REAL_LIST v_s]))"
    7.63  ;
    7.64  val sc = ((inst_abs thy) o term_of o the o (parse thy)) str;
    7.65  val str = 
    7.66 -"Script SolveSystemScript (es_::bool list) (vs_::real list) = \
    7.67 -\  (let es__ = ((Try (Rewrite_Set_Inst [(bdv_1, hd vs_),(bdv_2, hd (tl vs_))]\
    7.68 +"Script SolveSystemScript (es_::bool list) (v_s::real list) = \
    7.69 +\  (let es__ = ((Try (Rewrite_Set_Inst [(bdv_1, hd v_s),(bdv_2, hd (tl v_s))]\
    7.70  \                                 simplify_System_parenthesized False)) @@\
    7.71 -\               (Try (Rewrite_Set_Inst [(bdv_1, hd vs_),(bdv_2, hd (tl vs_))]\
    7.72 +\               (Try (Rewrite_Set_Inst [(bdv_1, hd v_s),(bdv_2, hd (tl v_s))]\
    7.73  \                                 simplify_System_parenthesized False))) es_\
    7.74  \   in (SubProblem (Biegelinie_,[linear,system],[no_met])\
    7.75 -\                  [BOOL_LIST es__, REAL_LIST vs_]))"
    7.76 +\                  [BOOL_LIST es__, REAL_LIST v_s]))"
    7.77  ;
    7.78  val sc = ((inst_abs thy) o term_of o the o (parse thy)) str;
    7.79  val str = 
    7.80 -"Script SolveSystemScript (es_::bool list) (vs_::real list) = \
    7.81 -\  (let es__ = ((Try (Rewrite_Set_Inst [(bdv_1, hd vs_),(bdv_2, hd (tl vs_))]\
    7.82 +"Script SolveSystemScript (es_::bool list) (v_s::real list) = \
    7.83 +\  (let es__ = ((Try (Rewrite_Set_Inst [(bdv_1, hd v_s),(bdv_2, hd (tl v_s))]\
    7.84  \                                 simplify_System_parenthesized False)) @@\
    7.85 -\               (Try (Rewrite_Set_Inst [(bdv_1, hd vs_),(bdv_2, hd (tl vs_))]\
    7.86 +\               (Try (Rewrite_Set_Inst [(bdv_1, hd v_s),(bdv_2, hd (tl v_s))]\
    7.87  \                                 simplify_System_parenthesized False)) @@\
    7.88 -\               (Try (Rewrite_Set_Inst [(bdv_1, hd vs_),(bdv_2, hd (tl vs_))]\
    7.89 +\               (Try (Rewrite_Set_Inst [(bdv_1, hd v_s),(bdv_2, hd (tl v_s))]\
    7.90  \                                 simplify_System_parenthesized False))) es_\
    7.91  \   in (SubProblem (Biegelinie_,[linear,system],[no_met])\
    7.92 -\                  [BOOL_LIST es__, REAL_LIST vs_]))"
    7.93 +\                  [BOOL_LIST es__, REAL_LIST v_s]))"
    7.94  ;
    7.95  val sc = ((inst_abs thy) o term_of o the o (parse thy)) str;
    7.96  val str = 
    7.97 -"Script SolveSystemScript (es_::bool list) (vs_::real list) = \
    7.98 -\  (let es__ = ((Try (Rewrite_Set_Inst [(bdv_1, hd vs_),(bdv_2, hd (tl vs_))]\
    7.99 +"Script SolveSystemScript (es_::bool list) (v_s::real list) = \
   7.100 +\  (let es__ = ((Try (Rewrite_Set_Inst [(bdv_1, hd v_s),(bdv_2, hd (tl v_s))]\
   7.101  \                                 simplify_System_parenthesized False)) @@\
   7.102  \               (Try (Rewrite_Set_Inst [] isolate_bdvs False)) @@\
   7.103 -\               (Try (Rewrite_Set_Inst [(bdv_1, hd vs_),(bdv_2, hd (tl vs_))]\
   7.104 +\               (Try (Rewrite_Set_Inst [(bdv_1, hd v_s),(bdv_2, hd (tl v_s))]\
   7.105  \                                 simplify_System_parenthesized False)) @@\
   7.106  \               (Try (Rewrite_Set order_system False))) es_\
   7.107  \   in (SubProblem (Biegelinie_,[linear,system],[no_met])\
   7.108 -\                  [BOOL_LIST es__, REAL_LIST vs_]))"
   7.109 +\                  [BOOL_LIST es__, REAL_LIST v_s]))"
   7.110  ;
   7.111  val sc = ((inst_abs thy) o term_of o the o (parse thy)) str;
   7.112  val str = 
   7.113 -"Script SolveSystemScript (es_::bool list) (vs_::real list) = \
   7.114 -\  (let es__ = ((Try (Rewrite_Set_Inst [(bdv_1, hd vs_),(bdv_2, hd (tl vs_))]\
   7.115 +"Script SolveSystemScript (es_::bool list) (v_s::real list) = \
   7.116 +\  (let es__ = ((Try (Rewrite_Set_Inst [(bdv_1, hd v_s),(bdv_2, hd (tl v_s))]\
   7.117  \                                 simplify_System_parenthesized False)) @@\
   7.118 -\               (Try (Rewrite_Set_Inst [(bdv_1, hd vs_)]\
   7.119 +\               (Try (Rewrite_Set_Inst [(bdv_1, hd v_s)]\
   7.120  \                                                    isolate_bdvs False)) @@\
   7.121 -\               (Try (Rewrite_Set_Inst [(bdv_1, hd vs_),(bdv_2, hd (tl vs_))]\
   7.122 +\               (Try (Rewrite_Set_Inst [(bdv_1, hd v_s),(bdv_2, hd (tl v_s))]\
   7.123  \                                 simplify_System_parenthesized False)) @@\
   7.124  \               (Try (Rewrite_Set order_system False))) es_\
   7.125  \   in (SubProblem (Biegelinie_,[linear,system],[no_met])\
   7.126 -\                  [BOOL_LIST es__, REAL_LIST vs_]))"
   7.127 +\                  [BOOL_LIST es__, REAL_LIST v_s]))"
   7.128  ;
   7.129  val sc = ((inst_abs thy) o term_of o the o (parse thy)) str;
   7.130  val str = 
   7.131 -"Script SolveSystemScript (es_::bool list) (vs_::real list) = \
   7.132 +"Script SolveSystemScript (es_::bool list) (v_s::real list) = \
   7.133  \  (let es__ = ((Try (Rewrite_Set simplify_System_parenthesized False)) @@\
   7.134 -\               (Try (Rewrite_Set_Inst [(bdv_1, hd vs_),(bdv_2, hd (tl vs_))]\
   7.135 +\               (Try (Rewrite_Set_Inst [(bdv_1, hd v_s),(bdv_2, hd (tl v_s))]\
   7.136  \                                                    isolate_bdvs False)) @@\
   7.137 -\               (Try (Rewrite_Set_Inst [(bdv_1, hd vs_),(bdv_2, hd (tl vs_))]\
   7.138 +\               (Try (Rewrite_Set_Inst [(bdv_1, hd v_s),(bdv_2, hd (tl v_s))]\
   7.139  \                                 simplify_System_parenthesized False)) @@\
   7.140  \               (Try (Rewrite_Set order_system False))) es_\
   7.141  \   in (SubProblem (Biegelinie_,[linear,system],[no_met])\
   7.142 -\                  [BOOL_LIST es__, REAL_LIST vs_]))"
   7.143 +\                  [BOOL_LIST es__, REAL_LIST v_s]))"
   7.144  ;
   7.145  val sc = ((inst_abs thy) o term_of o the o (parse thy)) str;
   7.146  (*---^^^-OK-----------------------------------------------------------------*)
   7.147 @@ -387,127 +387,127 @@
   7.148  "----------- script [EqSystem,top_down_substitution,2x2] Vers.1 --";
   7.149  "----------- script [EqSystem,top_down_substitution,2x2] Vers.1 --";
   7.150  val str = 
   7.151 -"Script SolveSystemScript (es_::bool list) (vs_::real list) = \
   7.152 -\  (let es__ = (Rewrite_Set_Inst [(bdv_1, hd vs_),(bdv_2, hd (tl vs_))]\
   7.153 +"Script SolveSystemScript (es_::bool list) (v_s::real list) = \
   7.154 +\  (let es__ = (Rewrite_Set_Inst [(bdv_1, hd v_s),(bdv_2, hd (tl v_s))]\
   7.155  \                                 simplify_System_parenthesized False) es_  \
   7.156  \   in ([]))";
   7.157  val sc = ((inst_abs thy) o term_of o the o (parse thy)) str;
   7.158  val str = 
   7.159 -"Script SolveSystemScript (es_::bool list) (vs_::real list) = \
   7.160 +"Script SolveSystemScript (es_::bool list) (v_s::real list) = \
   7.161  \  (let e1__ = Take (hd es_)                \
   7.162  \   in ([]))";
   7.163  val sc = ((inst_abs thy) o term_of o the o (parse thy)) str;
   7.164  val str = 
   7.165 -"Script SolveSystemScript (es_::bool list) (vs_::real list) = \
   7.166 +"Script SolveSystemScript (es_::bool list) (v_s::real list) = \
   7.167  \  (let e1__ = Take (hd es_);               \
   7.168  \       e1__ = Take (hd es_)                \
   7.169  \   in ([]))";
   7.170  val sc = ((inst_abs thy) o term_of o the o (parse thy)) str;
   7.171  val str = 
   7.172 -"Script SolveSystemScript (es_::bool list) (vs_::real list) = \
   7.173 +"Script SolveSystemScript (es_::bool list) (v_s::real list) = \
   7.174  \  (let e1__ = Take (hd es_);               \
   7.175  \       e1__ = (Take (hd es_))\
   7.176  \   in ([]))";
   7.177  val sc = ((inst_abs thy) o term_of o the o (parse thy)) str;
   7.178  val str = 
   7.179 -"Script SolveSystemScript (es_::bool list) (vs_::real list) = \
   7.180 +"Script SolveSystemScript (es_::bool list) (v_s::real list) = \
   7.181  \  (let e1__ = Take (hd es_);               \
   7.182  \       e1__ = ((Rewrite_Set order_system False)) e1__\
   7.183  \   in ([]))";
   7.184  val sc = ((inst_abs thy) o term_of o the o (parse thy)) str;
   7.185  (*--------------------------------------------------------------------------*)
   7.186  val str = 
   7.187 -"(Rewrite_Set_Inst [(bdv_1, hd vs_),(bdv_2, hd (tl vs_))]\
   7.188 +"(Rewrite_Set_Inst [(bdv_1, hd v_s),(bdv_2, hd (tl v_s))]\
   7.189  \                                           isolate_bdvs False) (e1__::bool)";
   7.190  val sc = ((inst_abs thy) o term_of o the o (parse thy)) str;
   7.191  (*--------------------------------------------------------------------------*)
   7.192  val str = 
   7.193 -"Script SolveSystemScript (es_::bool list) (vs_::real list) = \
   7.194 +"Script SolveSystemScript (es_::bool list) (v_s::real list) = \
   7.195  \  (let e1__ = Take (hd es_);               \
   7.196 -\       e1__ = ((Rewrite_Set_Inst [(bdv_1, hd vs_),(bdv_2, hd (tl vs_))]\
   7.197 +\       e1__ = ((Rewrite_Set_Inst [(bdv_1, hd v_s),(bdv_2, hd (tl v_s))]\
   7.198  \                                           isolate_bdvs False)) e1__\
   7.199  \   in ([]))";
   7.200  val sc = ((inst_abs thy) o term_of o the o (parse thy)) str;
   7.201  val str = 
   7.202 -"Script SolveSystemScript (es_::bool list) (vs_::real list) = \
   7.203 +"Script SolveSystemScript (es_::bool list) (v_s::real list) = \
   7.204  \  (let e1__ = Take (hd es_);               \
   7.205 -\       e1__ = ((Try (Rewrite_Set_Inst [(bdv_1, hd vs_),(bdv_2, hd (tl vs_))]\
   7.206 +\       e1__ = ((Try (Rewrite_Set_Inst [(bdv_1, hd v_s),(bdv_2, hd (tl v_s))]\
   7.207  \                                           isolate_bdvs False)) @@\
   7.208 -\               (Rewrite_Set_Inst [(bdv_1, hd vs_),(bdv_2, hd (tl vs_))]\
   7.209 +\               (Rewrite_Set_Inst [(bdv_1, hd v_s),(bdv_2, hd (tl v_s))]\
   7.210  \                                 simplify_System False)) e1__\
   7.211  \   in ([]))";
   7.212  val sc = ((inst_abs thy) o term_of o the o (parse thy)) str;
   7.213  val str = 
   7.214 -"Script SolveSystemScript (es_::bool list) (vs_::real list) = \
   7.215 +"Script SolveSystemScript (es_::bool list) (v_s::real list) = \
   7.216  \  (let e1__ = Take (hd es_);               \
   7.217 -\       e1__ = ((Try (Rewrite_Set_Inst [(bdv_1, hd vs_),(bdv_2, hd (tl vs_))]\
   7.218 +\       e1__ = ((Try (Rewrite_Set_Inst [(bdv_1, hd v_s),(bdv_2, hd (tl v_s))]\
   7.219  \                                           isolate_bdvs False)) @@\
   7.220 -\               (Try (Rewrite_Set_Inst [(bdv_1, hd vs_),(bdv_2, hd (tl vs_))]\
   7.221 +\               (Try (Rewrite_Set_Inst [(bdv_1, hd v_s),(bdv_2, hd (tl v_s))]\
   7.222  \                                 simplify_System False))) e1__\
   7.223  \   in ([]))";
   7.224  val sc = ((inst_abs thy) o term_of o the o (parse thy)) str;
   7.225  val str = 
   7.226 -"Script SolveSystemScript (es_::bool list) (vs_::real list) =                \
   7.227 +"Script SolveSystemScript (es_::bool list) (v_s::real list) =                \
   7.228  \  (let e1__ = Take (hd es_);                                                \
   7.229 -\       e1__ = ((Try (Rewrite_Set_Inst [(bdv_1, hd vs_),(bdv_2, hd (tl vs_))]\
   7.230 +\       e1__ = ((Try (Rewrite_Set_Inst [(bdv_1, hd v_s),(bdv_2, hd (tl v_s))]\
   7.231  \                                           isolate_bdvs False)) @@          \
   7.232 -\               (Try (Rewrite_Set_Inst [(bdv_1, hd vs_),(bdv_2, hd (tl vs_))]\
   7.233 +\               (Try (Rewrite_Set_Inst [(bdv_1, hd v_s),(bdv_2, hd (tl v_s))]\
   7.234  \                                 simplify_System False))) e1__;           \
   7.235  \       e2__ = Take (hd (tl es_))                                            \
   7.236  \   in ([]))";
   7.237  val sc = ((inst_abs thy) o term_of o the o (parse thy)) str;
   7.238  val str = 
   7.239 -"Script SolveSystemScript (es_::bool list) (vs_::real list) =                \
   7.240 +"Script SolveSystemScript (es_::bool list) (v_s::real list) =                \
   7.241  \  (let e1__ = Take (hd es_);                                                \
   7.242 -\       e1__ = ((Try (Rewrite_Set_Inst [(bdv_1, hd vs_),(bdv_2, hd (tl vs_))]\
   7.243 +\       e1__ = ((Try (Rewrite_Set_Inst [(bdv_1, hd v_s),(bdv_2, hd (tl v_s))]\
   7.244  \                                           isolate_bdvs False)) @@          \
   7.245 -\               (Try (Rewrite_Set_Inst [(bdv_1, hd vs_),(bdv_2, hd (tl vs_))]\
   7.246 +\               (Try (Rewrite_Set_Inst [(bdv_1, hd v_s),(bdv_2, hd (tl v_s))]\
   7.247  \                                 simplify_System False))) e1__;           \
   7.248  \       e2__ = Take (hd (tl es_));                                           \
   7.249  \       e2__ = Substitute [e1__] e2__                                       \
   7.250  \   in ([]))";
   7.251  val sc = ((inst_abs thy) o term_of o the o (parse thy)) str;
   7.252  val str = 
   7.253 -"Script SolveSystemScript (es_::bool list) (vs_::real list) =                \
   7.254 +"Script SolveSystemScript (es_::bool list) (v_s::real list) =                \
   7.255  \  (let e1__ = Take (hd es_);                                                \
   7.256 -\       e1__ = ((Try (Rewrite_Set_Inst [(bdv_1, hd vs_),(bdv_2, hd (tl vs_))]\
   7.257 +\       e1__ = ((Try (Rewrite_Set_Inst [(bdv_1, hd v_s),(bdv_2, hd (tl v_s))]\
   7.258  \                                           isolate_bdvs False)) @@          \
   7.259 -\               (Try (Rewrite_Set_Inst [(bdv_1, hd vs_),(bdv_2, hd (tl vs_))]\
   7.260 +\               (Try (Rewrite_Set_Inst [(bdv_1, hd v_s),(bdv_2, hd (tl v_s))]\
   7.261  \                                 simplify_System False))) e1__;           \
   7.262  \       e2__ = Take (hd (tl es_));                                           \
   7.263  \       e2__ = ((Substitute [e1__])) e2__                                  \
   7.264  \   in ([]))";
   7.265  val sc = ((inst_abs thy) o term_of o the o (parse thy)) str;
   7.266  val str = 
   7.267 -"Script SolveSystemScript (es_::bool list) (vs_::real list) =                \
   7.268 +"Script SolveSystemScript (es_::bool list) (v_s::real list) =                \
   7.269  \  (let e1__ = Take (hd es_);                                                \
   7.270 -\       e1__ = ((Try (Rewrite_Set_Inst [(bdv_1, hd vs_),(bdv_2, hd (tl vs_))]\
   7.271 +\       e1__ = ((Try (Rewrite_Set_Inst [(bdv_1, hd v_s),(bdv_2, hd (tl v_s))]\
   7.272  \                                      isolate_bdvs False)) @@               \
   7.273 -\               (Try (Rewrite_Set_Inst [(bdv_1, hd vs_),(bdv_2, hd (tl vs_))]\
   7.274 +\               (Try (Rewrite_Set_Inst [(bdv_1, hd v_s),(bdv_2, hd (tl v_s))]\
   7.275  \                                 simplify_System False))) e1__;           \
   7.276  \       e2__ = Take (hd (tl es_));                                           \
   7.277  \       e2__ = ((Substitute [e1__]) @@                                       \
   7.278 -\               (Try (Rewrite_Set_Inst [(bdv_1, hd vs_),(bdv_2, hd (tl vs_))]\
   7.279 +\               (Try (Rewrite_Set_Inst [(bdv_1, hd v_s),(bdv_2, hd (tl v_s))]\
   7.280  \                                      isolate_bdvs False)) @@               \
   7.281 -\               (Try (Rewrite_Set_Inst [(bdv_1, hd vs_),(bdv_2, hd (tl vs_))]\
   7.282 +\               (Try (Rewrite_Set_Inst [(bdv_1, hd v_s),(bdv_2, hd (tl v_s))]\
   7.283  \                                 simplify_System False))) e2__            \
   7.284  \   in [e1__, e2__])"
   7.285  ;
   7.286  val sc = ((inst_abs thy) o term_of o the o (parse thy)) str;
   7.287  val str = 
   7.288 -"Script SolveSystemScript (es_::bool list) (vs_::real list) =                \
   7.289 +"Script SolveSystemScript (es_::bool list) (v_s::real list) =                \
   7.290  \  (let e1__ = Take (hd es_);                                                \
   7.291 -\       e1__ = ((Try (Rewrite_Set_Inst [(bdv_1, hd vs_),(bdv_2, hd (tl vs_))]\
   7.292 +\       e1__ = ((Try (Rewrite_Set_Inst [(bdv_1, hd v_s),(bdv_2, hd (tl v_s))]\
   7.293  \                                      isolate_bdvs False)) @@               \
   7.294 -\               (Try (Rewrite_Set_Inst [(bdv_1, hd vs_),(bdv_2, hd (tl vs_))]\
   7.295 +\               (Try (Rewrite_Set_Inst [(bdv_1, hd v_s),(bdv_2, hd (tl v_s))]\
   7.296  \                                 simplify_System False))) e1__;           \
   7.297  \       e2__ = Take (hd (tl es_));                                           \
   7.298  \       e2__ = ((Substitute [e1__]) @@                                       \
   7.299 -\               (Try (Rewrite_Set_Inst [(bdv_1, hd vs_),(bdv_2, hd (tl vs_))]\
   7.300 +\               (Try (Rewrite_Set_Inst [(bdv_1, hd v_s),(bdv_2, hd (tl v_s))]\
   7.301  \                                 simplify_System_parenthesized False)) @@ \
   7.302 -\               (Try (Rewrite_Set_Inst [(bdv_1, hd vs_),(bdv_2, hd (tl vs_))]\
   7.303 +\               (Try (Rewrite_Set_Inst [(bdv_1, hd v_s),(bdv_2, hd (tl v_s))]\
   7.304  \                                      isolate_bdvs False)) @@               \
   7.305 -\               (Try (Rewrite_Set_Inst [(bdv_1, hd vs_),(bdv_2, hd (tl vs_))]\
   7.306 +\               (Try (Rewrite_Set_Inst [(bdv_1, hd v_s),(bdv_2, hd (tl v_s))]\
   7.307  \                                 simplify_System False)) @@               \
   7.308  \               (Try (Rewrite_Set order_system False))) e2__                 \
   7.309  \   in [e1__, e2__])"
   7.310 @@ -515,19 +515,19 @@
   7.311  val sc = ((inst_abs thy) o term_of o the o (parse thy)) str;
   7.312  (*---^^^-OK-----------------------------------------------------------------*)
   7.313  val str = 
   7.314 -"Script SolveSystemScript (es_::bool list) (vs_::real list) =                \
   7.315 +"Script SolveSystemScript (es_::bool list) (v_s::real list) =                \
   7.316  \  (let e1__ = Take (hd es_);                                                \
   7.317 -\       e1__ = ((Try (Rewrite_Set_Inst [(bdv_1, hd vs_),(bdv_2, hd (tl vs_))]\
   7.318 +\       e1__ = ((Try (Rewrite_Set_Inst [(bdv_1, hd v_s),(bdv_2, hd (tl v_s))]\
   7.319  \                                      isolate_bdvs False)) @@               \
   7.320 -\               (Try (Rewrite_Set_Inst [(bdv_1, hd vs_),(bdv_2, hd (tl vs_))]\
   7.321 +\               (Try (Rewrite_Set_Inst [(bdv_1, hd v_s),(bdv_2, hd (tl v_s))]\
   7.322  \                                 simplify_System False))) e1__;           \
   7.323  \       e2__ = Take (hd (tl es_));                                           \
   7.324  \       e2__ = ((Substitute [e1__]) @@                                       \
   7.325 -\               (Try (Rewrite_Set_Inst [(bdv_1, hd vs_),(bdv_2, hd (tl vs_))]\
   7.326 +\               (Try (Rewrite_Set_Inst [(bdv_1, hd v_s),(bdv_2, hd (tl v_s))]\
   7.327  \                                 simplify_System_parenthesized False)) @@ \
   7.328 -\               (Try (Rewrite_Set_Inst [(bdv_1, hd vs_),(bdv_2, hd (tl vs_))]\
   7.329 +\               (Try (Rewrite_Set_Inst [(bdv_1, hd v_s),(bdv_2, hd (tl v_s))]\
   7.330  \                                      isolate_bdvs False)) @@               \
   7.331 -\               (Try (Rewrite_Set_Inst [(bdv_1, hd vs_),(bdv_2, hd (tl vs_))]\
   7.332 +\               (Try (Rewrite_Set_Inst [(bdv_1, hd v_s),(bdv_2, hd (tl v_s))]\
   7.333  \                                 simplify_System False))) e2__;           \
   7.334  \       es__ = Take [e1__, e2__]\
   7.335  \   in (Try (Rewrite_Set order_system False)) es__)"
   7.336 @@ -540,14 +540,14 @@
   7.337  "----------- script [EqSystem,top_down_substitution,2x2] Vers.2 --";
   7.338  "----------- script [EqSystem,top_down_substitution,2x2] Vers.2 --";
   7.339  val str = 
   7.340 -"Script SolveSystemScript (es_::bool list) (vs_::real list) = \
   7.341 +"Script SolveSystemScript (es_::bool list) (v_s::real list) = \
   7.342  \  (let es__ = Take es_;   \
   7.343  \       e1__ = hd es__\
   7.344  \   in ([]))"
   7.345  ;
   7.346  val sc = ((inst_abs thy) o term_of o the o (parse thy)) str;
   7.347  val str = 
   7.348 -"Script SolveSystemScript (es_::bool list) (vs_::real list) = \
   7.349 +"Script SolveSystemScript (es_::bool list) (v_s::real list) = \
   7.350  \  (let es__ = Take es_;   \
   7.351  \       e1__ = hd es__;    \
   7.352  \       e2__ = hd (tl es__)\
   7.353 @@ -555,7 +555,7 @@
   7.354  ;
   7.355  val sc = ((inst_abs thy) o term_of o the o (parse thy)) str;
   7.356  val str = 
   7.357 -"Script SolveSystemScript (es_::bool list) (vs_::real list) = \
   7.358 +"Script SolveSystemScript (es_::bool list) (v_s::real list) = \
   7.359  \  (let es__ = Take es_;   \
   7.360  \       e1__ = hd es__;    \
   7.361  \       e2__ = hd (tl es__);\
   7.362 @@ -564,7 +564,7 @@
   7.363  ;
   7.364  val sc = ((inst_abs thy) o term_of o the o (parse thy)) str;
   7.365  val str = 
   7.366 -"Script SolveSystemScript (es_::bool list) (vs_::real list) = \
   7.367 +"Script SolveSystemScript (es_::bool list) (v_s::real list) = \
   7.368  \  (let es__ = Take es_;   \
   7.369  \       e1__ = hd es__;    \
   7.370  \       e2__ = hd (tl es__);\
   7.371 @@ -573,87 +573,87 @@
   7.372  ;
   7.373  val sc = ((inst_abs thy) o term_of o the o (parse thy)) str;
   7.374  val str = 
   7.375 -"Script SolveSystemScript (es_::bool list) (vs_::real list) = \
   7.376 +"Script SolveSystemScript (es_::bool list) (v_s::real list) = \
   7.377  \  (let es__ = Take es_;   \
   7.378  \       e1__ = hd es__;    \
   7.379  \       e2__ = hd (tl es__);\
   7.380  \       es__ = [e1__, Substitute [e1__] e2__];\
   7.381 -\       es__ = (Try (Rewrite_Set_Inst [(bdv_1, hd vs_),(bdv_2, hd (tl vs_))]\
   7.382 +\       es__ = (Try (Rewrite_Set_Inst [(bdv_1, hd v_s),(bdv_2, hd (tl v_s))]\
   7.383  \                                 simplify_System False)) es__            \
   7.384  \   in ([]))"
   7.385  ;
   7.386  val sc = ((inst_abs thy) o term_of o the o (parse thy)) str;
   7.387  val str = 
   7.388 -"Script SolveSystemScript (es_::bool list) (vs_::real list) = \
   7.389 +"Script SolveSystemScript (es_::bool list) (v_s::real list) = \
   7.390  \  (let es__ = Take es_;   \
   7.391  \       e1__ = hd es__;    \
   7.392  \       e2__ = hd (tl es__);\
   7.393  \       es__ = [e1__, Substitute [e1__] e2__];\
   7.394 -\       es__ = ((Try (Rewrite_Set_Inst [(bdv_1, hd vs_),(bdv_2, hd (tl vs_))]\
   7.395 +\       es__ = ((Try (Rewrite_Set_Inst [(bdv_1, hd v_s),(bdv_2, hd (tl v_s))]\
   7.396  \                                      isolate_bdvs False)) @@               \
   7.397 -\               (Try (Rewrite_Set_Inst [(bdv_1, hd vs_),(bdv_2, hd (tl vs_))]\
   7.398 +\               (Try (Rewrite_Set_Inst [(bdv_1, hd v_s),(bdv_2, hd (tl v_s))]\
   7.399  \                                 simplify_System False))) es__            \
   7.400  \   in ([]))"
   7.401  ;
   7.402  val sc = ((inst_abs thy) o term_of o the o (parse thy)) str;
   7.403  val str = 
   7.404 -"Script SolveSystemScript (es_::bool list) (vs_::real list) = \
   7.405 +"Script SolveSystemScript (es_::bool list) (v_s::real list) = \
   7.406  \  (let es__ = Take es_;   \
   7.407  \       e1__ = hd es__;    \
   7.408  \       e2__ = hd (tl es__);\
   7.409  \       es__ = [e1__, Substitute [e1__] e2__];\
   7.410 -\       es__ = ((Try (Rewrite_Set_Inst [(bdv_1, hd vs_),(bdv_2, hd (tl vs_))]\
   7.411 +\       es__ = ((Try (Rewrite_Set_Inst [(bdv_1, hd v_s),(bdv_2, hd (tl v_s))]\
   7.412  \                                 simplify_System_parenthesized False)) @@  \
   7.413 -\               (Try (Rewrite_Set_Inst [(bdv_1, hd vs_),(bdv_2, hd (tl vs_))]\
   7.414 +\               (Try (Rewrite_Set_Inst [(bdv_1, hd v_s),(bdv_2, hd (tl v_s))]\
   7.415  \                                      isolate_bdvs False)) @@               \
   7.416 -\               (Try (Rewrite_Set_Inst [(bdv_1, hd vs_),(bdv_2, hd (tl vs_))]\
   7.417 +\               (Try (Rewrite_Set_Inst [(bdv_1, hd v_s),(bdv_2, hd (tl v_s))]\
   7.418  \                                 simplify_System False))) es__            \
   7.419  \   in ([]))"
   7.420  ;
   7.421  val sc = ((inst_abs thy) o term_of o the o (parse thy)) str;
   7.422  val str = 
   7.423 -"Script SolveSystemScript (es_::bool list) (vs_::real list) = \
   7.424 +"Script SolveSystemScript (es_::bool list) (v_s::real list) = \
   7.425  \  (let es__ = Take es_;                                                     \
   7.426  \       e1__ = hd es__;                                                      \
   7.427  \       e2__ = hd (tl es__);                                                 \
   7.428  \       es__ = [e1__, Substitute [e1__] e2__];                               \
   7.429 -\       es__ = ((Try (Rewrite_Set_Inst [(bdv_1, hd vs_),(bdv_2, hd (tl vs_))]\
   7.430 +\       es__ = ((Try (Rewrite_Set_Inst [(bdv_1, hd v_s),(bdv_2, hd (tl v_s))]\
   7.431  \                                 simplify_System_parenthesized False)) @@  \
   7.432 -\               (Try (Rewrite_Set_Inst [(bdv_1, hd vs_),(bdv_2, hd (tl vs_))]\
   7.433 +\               (Try (Rewrite_Set_Inst [(bdv_1, hd v_s),(bdv_2, hd (tl v_s))]\
   7.434  \                                      isolate_bdvs False))              @@  \
   7.435 -\               (Try (Rewrite_Set_Inst [(bdv_1, hd vs_),(bdv_2, hd (tl vs_))]\
   7.436 +\               (Try (Rewrite_Set_Inst [(bdv_1, hd v_s),(bdv_2, hd (tl v_s))]\
   7.437  \                                 simplify_System False))) es__            \
   7.438  \   in es__)"
   7.439  ;
   7.440  val sc = ((inst_abs thy) o term_of o the o (parse thy)) str;
   7.441  val str = 
   7.442 -"Script SolveSystemScript (es_::bool list) (vs_::real list) =         \
   7.443 +"Script SolveSystemScript (es_::bool list) (v_s::real list) =         \
   7.444  \  (let es__ = Take es_;                                              \
   7.445  \       e1__ = hd es__;                                               \
   7.446  \       e2__ = hd (tl es__);                                          \
   7.447  \       es__ = [e1__, Substitute [e1__] e2__]                         \
   7.448 -\   in ((Try (Rewrite_Set_Inst [(bdv_1, hd vs_),(bdv_2, hd (tl vs_))]\
   7.449 +\   in ((Try (Rewrite_Set_Inst [(bdv_1, hd v_s),(bdv_2, hd (tl v_s))]\
   7.450  \                                 simplify_System_parenthesized False)) @@   \
   7.451 -\       (Try (Rewrite_Set_Inst [(bdv_1, hd vs_),(bdv_2, hd (tl vs_))] \
   7.452 +\       (Try (Rewrite_Set_Inst [(bdv_1, hd v_s),(bdv_2, hd (tl v_s))] \
   7.453  \                              isolate_bdvs False))              @@   \
   7.454 -\       (Try (Rewrite_Set_Inst [(bdv_1, hd vs_),(bdv_2, hd (tl vs_))]\
   7.455 +\       (Try (Rewrite_Set_Inst [(bdv_1, hd v_s),(bdv_2, hd (tl v_s))]\
   7.456  \                                 simplify_System False))) es__)"
   7.457  ;
   7.458  val sc = ((inst_abs thy) o term_of o the o (parse thy)) str;
   7.459  (*---^^^-OK-----------------------------------------------------------------*)
   7.460  val str = 
   7.461 -"Script SolveSystemScript (es_::bool list) (vs_::real list) =         \
   7.462 +"Script SolveSystemScript (es_::bool list) (v_s::real list) =         \
   7.463  \  (let es__ = Take es_;                                              \
   7.464  \       e1__ = hd es__;                                               \
   7.465  \       e2__ = hd (tl es__);                                          \
   7.466  \       es__ = [e1__, Substitute [e1__] e2__]                         "^
   7.467  (* this        ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ is a script-'Expr'
   7.468     which is not yet searched for 'STac's; thus this script does not yet work*)
   7.469 -"   in ((Try (Rewrite_Set_Inst [(bdv_1, hd vs_),(bdv_2, hd (tl vs_))]\
   7.470 +"   in ((Try (Rewrite_Set_Inst [(bdv_1, hd v_s),(bdv_2, hd (tl v_s))]\
   7.471  \                                 simplify_System_parenthesized False)) @@   \
   7.472 -\       (Try (Rewrite_Set_Inst [(bdv_1, hd vs_),(bdv_2, hd (tl vs_))] \
   7.473 +\       (Try (Rewrite_Set_Inst [(bdv_1, hd v_s),(bdv_2, hd (tl v_s))] \
   7.474  \                              isolate_bdvs False))              @@   \
   7.475 -\       (Try (Rewrite_Set_Inst [(bdv_1, hd vs_),(bdv_2, hd (tl vs_))]\
   7.476 +\       (Try (Rewrite_Set_Inst [(bdv_1, hd v_s),(bdv_2, hd (tl v_s))]\
   7.477  \                                 simplify_System False))) es__)"
   7.478  ;
   7.479  val sc = ((inst_abs thy) o term_of o the o (parse thy)) str;
   7.480 @@ -791,14 +791,14 @@
   7.481  (* val (thy, (pblID, dsc_dats: (string * (string list)) list, 
   7.482  		  ev:rls, ca: string option, metIDs:metID list)) =
   7.483         (EqSystem.thy, (["system"],
   7.484 -		       [("#Given" ,["equalities es_", "solveForVars vs_"]),
   7.485 +		       [("#Given" ,["equalities es_", "solveForVars v_s"]),
   7.486  			("#Find"  ,["solution ss___"](*___ is copy-named*))
   7.487  			],
   7.488  		       append_rls "e_rls" e_rls [(*for preds in where_*)], 
   7.489 -		       SOME "solveSystem es_ vs_", 
   7.490 +		       SOME "solveSystem es_ v_s", 
   7.491  		       []));
   7.492     *)
   7.493 -> val [("#Given", [equalities_es_, "solveForVars vs_"])] = gi;
   7.494 +> val [("#Given", [equalities_es_, "solveForVars v_s"])] = gi;
   7.495  val equalities_es_ = "equalities es_" : string
   7.496  > val (dd, ii) = (split_did o term_of o the o (parse thy)) equalities_es_;
   7.497  > show_types:=true; term2str ii; show_types:=false;
   7.498 @@ -819,7 +819,7 @@
   7.499   [0 = -1 * q_0 * 0 ^^^ 2 / 2 + 0 * c + c_2,
   7.500    0 = -1 * q_0 * L ^^^ 2 / 2 + L * c + c_2] ,(es_, [[0 = -1 * q_0 * 0 ^^^ 2 / 2 + 0 * c + c_2,
   7.501   0 = -1 * q_0 * L ^^^ 2 / 2 + L * c + c_2]])),
   7.502 -(2 ,[1] ,true ,#Given ,Cor solveForVars [c, c_2] ,(vs_, [[c, c_2]])),
   7.503 +(2 ,[1] ,true ,#Given ,Cor solveForVars [c, c_2] ,(v_s, [[c, c_2]])),
   7.504  (3 ,[1] ,true ,#Find ,Cor solution L ,(ss___, [L]))]
   7.505  
   7.506  > (writeln o pres2str) pre';
   7.507 @@ -837,7 +837,7 @@
   7.508  ["
   7.509  (es_, [0 = -1 * q_0 * 0 ^^^ 2 / 2 + 0 * c + c_2,
   7.510   0 = -1 * q_0 * L ^^^ 2 / 2 + L * c + c_2])","
   7.511 -(vs_, [c, c_2])","
   7.512 +(v_s, [c, c_2])","
   7.513  (ss___, L)"]
   7.514  
   7.515  > val es_ = (fst o hd) env;
   7.516 @@ -899,7 +899,7 @@
   7.517      (writeln o (itms2str_ (thy2ctxt "Isac"))) probl;
   7.518  (*[
   7.519  (1 ,[1] ,true ,#Given ,Cor equalities [c_2 = 0, L * c + c_2 = q_0 * L ^^^ 2 / 2] ,(es_, [[c_2 = 0, L * c + c_2 = q_0 * L ^^^ 2 / 2]])),
   7.520 -(2 ,[1] ,true ,#Given ,Cor solveForVars [c, c_2] ,(vs_, [[c, c_2]])),
   7.521 +(2 ,[1] ,true ,#Given ,Cor solveForVars [c, c_2] ,(v_s, [[c, c_2]])),
   7.522  (3 ,[1] ,true ,#Find ,Cor solution ss___ ,(ss___, [ss___]))]
   7.523  *)
   7.524  val (p,_,f,nxt,_,pt) = me nxt p c pt;f2str f;
   7.525 @@ -968,7 +968,7 @@
   7.526      (writeln o (itms2str_ (thy2ctxt "Isac"))) probl;
   7.527  (*[
   7.528  (1 ,[1] ,true ,#Given ,Cor equalities [c_2 = 0, L * c + c_2 = q_0 * L ^^^ 2 / 2] ,(es_, [[c_2 = 0, L * c + c_2 = q_0 * L ^^^ 2 / 2]])),
   7.529 -(2 ,[1] ,true ,#Given ,Cor solveForVars [c, c_2] ,(vs_, [[c, c_2]])),
   7.530 +(2 ,[1] ,true ,#Given ,Cor solveForVars [c, c_2] ,(v_s, [[c, c_2]])),
   7.531  (3 ,[1] ,true ,#Find ,Cor solution ss___ ,(ss___, [ss___]))]
   7.532  *)
   7.533  val (p,_,f,nxt,_,pt) = me nxt p c pt;f2str f;
   7.534 @@ -1155,23 +1155,23 @@
   7.535  "--- scr [EqSystem,top_down_substitution,4x4] -- a saved trial";
   7.536  (*---vvv-this script failed with if ?!?-------------------------------------*) 
   7.537  val str = 
   7.538 -"Script SolveSystemScript (es_::bool list) (vs_::real list) =          \
   7.539 +"Script SolveSystemScript (es_::bool list) (v_s::real list) =          \
   7.540  \  (let e1_ = hd es_;                                                  \
   7.541 -\       v1_ = hd vs_;                                                  \
   7.542 +\       v1_ = hd v_s;                                                  \
   7.543  \       xxx = if lhs e1_ =!= v1_                                       \
   7.544  \             then 0=0                                                 \
   7.545  \             else let e1_ = Take e1_;                                 \
   7.546 -\                      e1_ = (Rewrite_Set_Inst [(bdv_1, hd vs_),       \
   7.547 -\                                               (bdv_2, hd (tl vs_))]  \
   7.548 +\                      e1_ = (Rewrite_Set_Inst [(bdv_1, hd v_s),       \
   7.549 +\                                               (bdv_2, hd (tl v_s))]  \
   7.550  \                                  isolate_bdvs False) e1_;            \
   7.551  \       e2_ = Take (hd (tl es_));                                      \
   7.552  \       e2_ = (Substitute [e1__]) e2_                                  \
   7.553  \    in [e1_, e2_])";
   7.554  (*val sc = ((inst_abs thy) o term_of o the o (parse thy)) str;*)
   7.555  val str = 
   7.556 -"Script SolveSystemScript (es_::bool list) (vs_::real list) =          \
   7.557 +"Script SolveSystemScript (es_::bool list) (v_s::real list) =          \
   7.558  \  (let e1_ = hd es_;                                                  \
   7.559 -\       v1_ = hd vs_;                                                  \
   7.560 +\       v1_ = hd v_s;                                                  \
   7.561  \       e2_ = Take (hd (tl es_));                                      \
   7.562  \       e2_ = (Substitute [e1__]) e2_                                  \
   7.563  \    in [e1_, e2_])";
   7.564 @@ -1179,9 +1179,9 @@
   7.565  (*---^^^-OK-----------------------------------------------------------------*)
   7.566  (*---vvv-NOT ok-------------------------------------------------------------*)
   7.567  val str = 
   7.568 -"Script SolveSystemScript (es_::bool list) (vs_::real list) =          \
   7.569 +"Script SolveSystemScript (es_::bool list) (v_s::real list) =          \
   7.570  \  (let e1_ = hd es_;                                                  \
   7.571 -\       v1_ = hd vs_;                                                  \
   7.572 +\       v1_ = hd v_s;                                                  \
   7.573  \       xxx = if ((lhs e1_) =!= v1_) then 1 else 2; \
   7.574  \       e2_ = Take (hd (tl es_));                                      \
   7.575  \       e2_ = (Substitute [e1__]) e2_                                  \
   7.576 @@ -1196,101 +1196,101 @@
   7.577  
   7.578  "--- scr [EqSystem,top_down_substitution,4x4] -- adapted only to 7.70";
   7.579  val str = 
   7.580 -"Script SolveSystemScript (es_::bool list) (vs_::real list) =                \
   7.581 +"Script SolveSystemScript (es_::bool list) (v_s::real list) =                \
   7.582  \  (let e2__ = Take (hd (tl es_));                                           \
   7.583  \       e2__ = ((Substitute [e1__]) @@                                       \
   7.584 -\               (Try (Rewrite_Set_Inst [(bdv_1, hd vs_),(bdv_2, hd (tl vs_))]\
   7.585 +\               (Try (Rewrite_Set_Inst [(bdv_1, hd v_s),(bdv_2, hd (tl v_s))]\
   7.586  \                                  simplify_System_parenthesized False)) @@  \
   7.587 -\               (Try (Rewrite_Set_Inst [(bdv_1, hd vs_),(bdv_2, hd (tl vs_))]\
   7.588 +\               (Try (Rewrite_Set_Inst [(bdv_1, hd v_s),(bdv_2, hd (tl v_s))]\
   7.589  \                                  isolate_bdvs False))                  @@  \
   7.590 -\               (Try (Rewrite_Set_Inst [(bdv_1, hd vs_),(bdv_2, hd (tl vs_))]\
   7.591 +\               (Try (Rewrite_Set_Inst [(bdv_1, hd v_s),(bdv_2, hd (tl v_s))]\
   7.592  \                                  simplify_System False)))             e2__;\
   7.593  \       es__ = Take [e1__, e2__]                                             \
   7.594  \   in (Try (Rewrite_Set order_system False)) es__)"
   7.595  val sc = ((inst_abs thy) o term_of o the o (parse thy)) str;
   7.596  val str = 
   7.597 -"Script SolveSystemScript (es_::bool list) (vs_::real list) =                \
   7.598 +"Script SolveSystemScript (es_::bool list) (v_s::real list) =                \
   7.599  \  (let e2__ = Take (nth_ 2 es_);                                           \
   7.600  \       e2__ = ((Substitute [e1__]) @@                                       \
   7.601 -\               (Try (Rewrite_Set_Inst [(bdv_1, hd vs_),(bdv_2, hd (tl vs_))]\
   7.602 +\               (Try (Rewrite_Set_Inst [(bdv_1, hd v_s),(bdv_2, hd (tl v_s))]\
   7.603  \                                  simplify_System_parenthesized False)) @@  \
   7.604 -\               (Try (Rewrite_Set_Inst [(bdv_1, hd vs_),(bdv_2, hd (tl vs_))]\
   7.605 +\               (Try (Rewrite_Set_Inst [(bdv_1, hd v_s),(bdv_2, hd (tl v_s))]\
   7.606  \                                  isolate_bdvs False))                  @@  \
   7.607 -\               (Try (Rewrite_Set_Inst [(bdv_1, hd vs_),(bdv_2, hd (tl vs_))]\
   7.608 +\               (Try (Rewrite_Set_Inst [(bdv_1, hd v_s),(bdv_2, hd (tl v_s))]\
   7.609  \                                  simplify_System False)))             e2__;\
   7.610  \       es__ = Take [e1__, e2__]                                             \
   7.611  \   in (Try (Rewrite_Set order_system False)) es__)"
   7.612  val sc = ((inst_abs thy) o term_of o the o (parse thy)) str;
   7.613  val str = 
   7.614 -"Script SolveSystemScript (es_::bool list) (vs_::real list) =                \
   7.615 +"Script SolveSystemScript (es_::bool list) (v_s::real list) =                \
   7.616  \  (let e2__ = Take (nth_ 2 es_);                                            \
   7.617  \       e2__ = ((Substitute [e1__]) @@                                       \
   7.618 -\               (Try (Rewrite_Set_Inst [(bdv_1, hd vs_),(bdv_2, nth_ 2 vs_)] \
   7.619 +\               (Try (Rewrite_Set_Inst [(bdv_1, hd v_s),(bdv_2, nth_ 2 v_s)] \
   7.620  \                                  simplify_System_parenthesized False)) @@  \
   7.621 -\               (Try (Rewrite_Set_Inst [(bdv_1, hd vs_),(bdv_2, nth_ 2 vs_)]\
   7.622 +\               (Try (Rewrite_Set_Inst [(bdv_1, hd v_s),(bdv_2, nth_ 2 v_s)]\
   7.623  \                                  isolate_bdvs False))                  @@  \
   7.624 -\               (Try (Rewrite_Set_Inst [(bdv_1, hd vs_),(bdv_2, nth_ 2 vs_)]\
   7.625 +\               (Try (Rewrite_Set_Inst [(bdv_1, hd v_s),(bdv_2, nth_ 2 v_s)]\
   7.626  \                                  simplify_System False)))             e2__;\
   7.627  \       es__ = Take [e1__, e2__]                                             \
   7.628  \   in (Try (Rewrite_Set order_system False)) es__)"
   7.629  val sc = ((inst_abs thy) o term_of o the o (parse thy)) str;
   7.630  val str = 
   7.631 -"Script SolveSystemScript (es_::bool list) (vs_::real list) =                 \
   7.632 +"Script SolveSystemScript (es_::bool list) (v_s::real list) =                 \
   7.633  \  (let e2__ = Take (nth_ 2 es_);                                             \
   7.634  \       e2__ = ((Substitute [e1__]) @@                                        \
   7.635 -\               (Try (Rewrite_Set_Inst [(bdv_1,nth_ 1 vs_),(bdv_2,nth_ 2 vs_),\
   7.636 -\                                       (bdv_3,nth_ 3 vs_),(bdv_4,nth_ 4 vs_)]\
   7.637 +\               (Try (Rewrite_Set_Inst [(bdv_1,nth_ 1 v_s),(bdv_2,nth_ 2 v_s),\
   7.638 +\                                       (bdv_3,nth_ 3 v_s),(bdv_4,nth_ 4 v_s)]\
   7.639  \                                  simplify_System_parenthesized False)) @@   \
   7.640 -\               (Try (Rewrite_Set_Inst [(bdv_1, hd vs_),(bdv_2, nth_ 2 vs_)]  \
   7.641 +\               (Try (Rewrite_Set_Inst [(bdv_1, hd v_s),(bdv_2, nth_ 2 v_s)]  \
   7.642  \                                  isolate_bdvs False))                  @@   \
   7.643 -\               (Try (Rewrite_Set_Inst [(bdv_1, hd vs_),(bdv_2, nth_ 2 vs_)]  \
   7.644 +\               (Try (Rewrite_Set_Inst [(bdv_1, hd v_s),(bdv_2, nth_ 2 v_s)]  \
   7.645  \                                  norm_Rational False)))             e2__;   \
   7.646  \       es__ = Take [e1__, e2__]                                              \
   7.647  \   in [])"
   7.648  val sc = ((inst_abs thy) o term_of o the o (parse thy)) str;
   7.649  val str = 
   7.650 -"Script SolveSystemScript (es_::bool list) (vs_::real list) =                 \
   7.651 +"Script SolveSystemScript (es_::bool list) (v_s::real list) =                 \
   7.652  \  (let e2_ = Take (nth_ 2 es_);                                             \
   7.653  \       e2_ = ((Substitute [e1_]) @@                                        \
   7.654 -\               (Try (Rewrite_Set_Inst [(bdv_1,nth_ 1 vs_),(bdv_2,nth_ 2 vs_),\
   7.655 -\                                       (bdv_3,nth_ 3 vs_),(bdv_4,nth_ 4 vs_)]\
   7.656 +\               (Try (Rewrite_Set_Inst [(bdv_1,nth_ 1 v_s),(bdv_2,nth_ 2 v_s),\
   7.657 +\                                       (bdv_3,nth_ 3 v_s),(bdv_4,nth_ 4 v_s)]\
   7.658  \                                  simplify_System_parenthesized False)) @@   \
   7.659 -\               (Try (Rewrite_Set_Inst [(bdv_1, hd vs_),(bdv_2, nth_ 2 vs_)]  \
   7.660 +\               (Try (Rewrite_Set_Inst [(bdv_1, hd v_s),(bdv_2, nth_ 2 v_s)]  \
   7.661  \                                  isolate_bdvs False))                  @@   \
   7.662 -\               (Try (Rewrite_Set_Inst [(bdv_1, hd vs_),(bdv_2, nth_ 2 vs_)]  \
   7.663 +\               (Try (Rewrite_Set_Inst [(bdv_1, hd v_s),(bdv_2, nth_ 2 v_s)]  \
   7.664  \                                  norm_Rational False)))             e2_;   \
   7.665  \       es_ = Take [e1_, e2_]                                              \
   7.666  \   in [e1_, e2_,e3_, e4_])"
   7.667  val sc = ((inst_abs thy) o term_of o the o (parse thy)) str;
   7.668  val str = 
   7.669 -"Script SolveSystemScript (es_::bool list) (vs_::real list) =                 \
   7.670 +"Script SolveSystemScript (es_::bool list) (v_s::real list) =                 \
   7.671  \  (let e2_ = Take (nth_ 2 es_);                                              \
   7.672  \       e2_ = ((Substitute [e1_]) @@                                          \
   7.673 -\               (Try (Rewrite_Set_Inst [(bdv_1,nth_ 1 vs_),(bdv_2,nth_ 2 vs_),\
   7.674 -\                                       (bdv_3,nth_ 3 vs_),(bdv_4,nth_ 4 vs_)]\
   7.675 +\               (Try (Rewrite_Set_Inst [(bdv_1,nth_ 1 v_s),(bdv_2,nth_ 2 v_s),\
   7.676 +\                                       (bdv_3,nth_ 3 v_s),(bdv_4,nth_ 4 v_s)]\
   7.677  \                                  simplify_System_parenthesized False)) @@   \
   7.678 -\               (Try (Rewrite_Set_Inst [(bdv_1,nth_ 1 vs_),(bdv_2,nth_ 2 vs_),\
   7.679 -\                                       (bdv_3,nth_ 3 vs_),(bdv_4,nth_ 4 vs_)]\
   7.680 +\               (Try (Rewrite_Set_Inst [(bdv_1,nth_ 1 v_s),(bdv_2,nth_ 2 v_s),\
   7.681 +\                                       (bdv_3,nth_ 3 v_s),(bdv_4,nth_ 4 v_s)]\
   7.682  \                                  isolate_bdvs False))                  @@   \
   7.683 -\               (Try (Rewrite_Set_Inst [(bdv_1,nth_ 1 vs_),(bdv_2,nth_ 2 vs_),\
   7.684 -\                                       (bdv_3,nth_ 3 vs_),(bdv_4,nth_ 4 vs_)]\
   7.685 +\               (Try (Rewrite_Set_Inst [(bdv_1,nth_ 1 v_s),(bdv_2,nth_ 2 v_s),\
   7.686 +\                                       (bdv_3,nth_ 3 v_s),(bdv_4,nth_ 4 v_s)]\
   7.687  \                                  norm_Rational False)))             e2_;    \
   7.688  \       es_ = Take [e1_, e2_]                                                 \
   7.689  \   in [e1_, e2_,e3_, e4_])"
   7.690  val sc = ((inst_abs thy) o term_of o the o (parse thy)) str;
   7.691  (*---^^^-OK-----------------------------------------------------------------*)
   7.692  val str = 
   7.693 -"Script SolveSystemScript (es_::bool list) (vs_::real list) =                 \
   7.694 +"Script SolveSystemScript (es_::bool list) (v_s::real list) =                 \
   7.695  \  (let e2_ = Take (nth_ 2 es_);                                              \
   7.696  \       e2_ = ((Substitute [e1_]) @@                                          \
   7.697 -\               (Try (Rewrite_Set_Inst [(bdv_1,nth_ 1 vs_),(bdv_2,nth_ 2 vs_),\
   7.698 -\                                       (bdv_3,nth_ 3 vs_),(bdv_4,nth_ 4 vs_)]\
   7.699 +\               (Try (Rewrite_Set_Inst [(bdv_1,nth_ 1 v_s),(bdv_2,nth_ 2 v_s),\
   7.700 +\                                       (bdv_3,nth_ 3 v_s),(bdv_4,nth_ 4 v_s)]\
   7.701  \                                  simplify_System_parenthesized False)) @@   \
   7.702 -\               (Try (Rewrite_Set_Inst [(bdv_1,nth_ 1 vs_),(bdv_2,nth_ 2 vs_),\
   7.703 -\                                       (bdv_3,nth_ 3 vs_),(bdv_4,nth_ 4 vs_)]\
   7.704 +\               (Try (Rewrite_Set_Inst [(bdv_1,nth_ 1 v_s),(bdv_2,nth_ 2 v_s),\
   7.705 +\                                       (bdv_3,nth_ 3 v_s),(bdv_4,nth_ 4 v_s)]\
   7.706  \                                  isolate_bdvs False))                  @@   \
   7.707 -\               (Try (Rewrite_Set_Inst [(bdv_1,nth_ 1 vs_),(bdv_2,nth_ 2 vs_),\
   7.708 -\                                       (bdv_3,nth_ 3 vs_),(bdv_4,nth_ 4 vs_)]\
   7.709 +\               (Try (Rewrite_Set_Inst [(bdv_1,nth_ 1 v_s),(bdv_2,nth_ 2 v_s),\
   7.710 +\                                       (bdv_3,nth_ 3 v_s),(bdv_4,nth_ 4 v_s)]\
   7.711  \                                  norm_Rational False)))             e2_     \
   7.712  \   in [e1_, e2_, nth_ 3 es_, nth_ 4 es_])"
   7.713  val sc = ((inst_abs thy) o term_of o the o (parse thy)) str;